X now becomes X-Y. If you want to rotate around some other point, do as BCullis said: subtract the center of rotation, then rotate around the origin, then add the center of rotation back. Does rotate around the origin mean around 0 0? It is commonly measured in degrees per second . When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. Every point makes a circle around the center: Here a triangle is rotated around the point marked with a "+" Try It Yourself. First we must define the axis of Rotation by 2 points - P1, P2 then do the following: 1. If this triangle is rotated 90 counterclockwise, find the vertices of the rotated figure and graph. Usually, you will be asked to rotate a shape around the origin, which is the point (0, 0) on a coordinate plane. Hence, this rotation is analogous to a 2D rotation in the y-z plane. be the corresponding point after a rotation around one of the coordinate axis has been applied. Rotation about the x-axis by an angle x, counterclockwise (looking along the x-axis towards the origin). . "point" is your point a, "center" is your point b. So, Let's get into this article!

The Right Way Equations 1 and 2 show the right way to rotate a point around the origin: x1 = x0 cos ( ) - y0 sin ( ) (Equation 1) y1 = x0 sin ( ) + y0 cos ( ) (Equation 2) If we plug in our example point of ( x0, y0) = (4, 3) and = 30, we get the answer ( x1, y1) = (1.964, 4.598), the same as before. If you use that formula with 0.707 for x and y you will find its roughly 1.0. Rotation about the x-axis by an angle x, counterclockwise (looking along the x-axis towards the origin). There is a definite center point in the rotation, and everything else revolves around that point. High School Physics Chapter 6 Section 1 It is a mechanical angle rather than an aerodynamic angle: In the absence of induced flow and/or aircraft airspeed, angle of attack and angle of incidence are the same Threads: 9 en "Angle of rotation ", angle through which the sample is turned about its mean vertical from any arbitrarily established position . Does rotate around the origin mean around 0 0? Rotate so that the rotation axis is aligned with one of the principle coordinate axes. I want to make a robot rotate around a point of origin in 2D space using data from the Teleporter service. double x1 = point.x - center.x; double y1 = point.y - center.y; double x2 = x1 * Math.cos (angle) - y1 * Math.sin (angle)); double y2 = x1 * Math.sin (angle) + y1 * Math.cos (angle)); point.x = x2 + center.x; point.y = y2 + center.y; This approach uses rotation matrices. =sr. So, the 180-degree rotation about the origin in both directions is the same and we make both h and k negative. Draw P' on your graph paper. conclude with the desired result of 3D rotation around a major axis. If you wanted to rotate that point around the origin, the coordinates of the new point would be located at (x',y'). nfries88 . Cancel Save. (. Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. The point is, that you're shifting the coordinate system, not the point. In mathematics, rotation is a transformation that revolves around a figure around a fixed point called the center of rotation. Then P0= R xPwhere the rotation matrix, R x,is given by: R x= 2 6 6 4 1 0 0 . In this lesson we'll look at how the rotation of a figure in a coordinate plane determines where it's located. A translation amongst x and y can be defined as: T ( x, y) = [ 1 0 x 0 1 y 0 0 1] As I understand, the rotation matrix around an arbitrary point, can be expressed as moving the rotation point to the origin, rotating around the origin and moving back to the original position. You may need to tap the screen to focus the mouse. To find angular velocity you would take the derivative of angular displacement in respect to time. Let P (x, y) be a point on the XY plane. Rotation: Rotation refers to rotating a point. This means that we a figure is rotated in a 180 . Cartesian and spherical coordinates are two ways of representing exactly the same Calculating Rotation Point. Find; Find and; Substitute and into and; Substitute the expression for and into in the given equation, and then simplify. Translate X to Y, so Y becomes the new origin. A rotation is a type of transformation that moves a figure around a central rotation point, called the point of rotation. Usually, you will be asked to rotate a shape around the origin, which is the point (0, 0) on a coordinate plane. When the point M (h, k) is rotating through 180, about the origin in a Counterclockwise or clockwise direction, then it takes the new position of the point M' (-h, -k). 3. R = [ cos ( ) sin ( ) 0 sin ( ) cos ( ) 0 0 0 1] with the angle and the rotation being counter-clockwise. This math worksheet was created on 2015-02-25 and has been viewed 2 times this week and 13 times this month. You can rotate shapes 90, 180, or 270 degrees around the origin using three basic formulas. To put it another way, rotation is the motion of a rigid body around a fixed point. Specify the start point and endpoint of the axis about which the objects are to be rotated (2 and 3). It is based on rotation or motion of objects around the centre of the axis. Geometry of rotation. Consider a point A rotated about the center C. Step 1: We change A to A1=A-C Step 2: We apply the rule for rotation of point A1 about origin to get A2 (a) 90 anticlockwise (x,y)-> (-y,x) (b . around a point. Completing the proof. The idea is to have an sprite "orbiting" around another sprite . Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. However, during the development of Muster my Monsters I need to perform rotations around arbitrary points. Rotating a shape 180 about the origin Squares up become squares down In 3D Rotation we also have to define the angle of Rotation with the axis of Rotation. x = x cos y sin y = y cos + x sin Where is the angle of rotation Rotating about a point in 2-dimensional space Maths Geometry rotation transformation Imagine a point located at (x,y). ( 2 votes) Cesare Fusari 7 years ago I'm a bit confused. So, if a line has the coordinates 2,4 and 4,5, it would rotate to -4,-2 and -5,-4. The above formula will rotate the point around the origin. Rotation is a circular motion around the particular axis of rotation or point of rotation. The rotation formula is used to find the position of the point after rotation. For example, (2,5) becomes (5,2). be the corresponding point after a rotation around one of the coordinate axis has been applied. These matrices are left-side multiplicated with vector positions, so the order of multiplication is from right to left - on the right side is the first operation, on the . This material shows an algebraic method to find the rotation (90, 180, 270 anticlockwise) of a point A about any point C which is not the origin. The angle of rotation is the arc length divided by the radius of curvature. In this example, we rotate a jet sprite to face the position of the mouse. Use a protractor to measure the specified angle counterclockwise. When points A, B, C are on a line, the ratio AC/AB is taken to be a signed ratio, which is negative is A is between B and C. Formula for rotation of a point by 90 degrees (counter-clockwise) Draw on graph paper the point P with coordinates (3,4). . The angle of rotation is often measured by using a unit called the radian. The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-clockwise) direction Rotation Matrices via Euler Parameters Euler Parameters where the axis of rotation is a unit vector, , and the angle of rotation about that axis is, Calculate the relative angle at the knee and the absolute angles of the . The x component of the point remains the same. Understand how we can derive a formula for the rotation of any point around the origin. Given a translation (specified by a 2D vector) and a rotation (specified by a scalar angle in radians) how do we calculate the rotation point P ? To Rotate a 3D Object Around an Axis Click Home tab > Modify panel > Rotate 3D. So you don't actually shift the point to the origin, you shift the origin to the point, and then back. Here you can drag the pin and try different shapes: The size and form of the item and its . In the figure above, the wind rotates the blades of a windmill. Geometry - Transformation - Rotation not around originHow do you rotate a shape around a point other than the origin?This geometry video explores the rotatin. These matrices are left-side multiplicated with vector positions, so the order of multiplication is from right to left - on the right side is the first operation, on the . Completing the proof If you're seeing this message, it means we're having trouble loading external resources on our website. The rotated vector has coordinates \((x_2, y_2)\) On the right, a parallelogram rotates around the red dot. I was under the impression that in order to rotate on a sphere (IE, for the point to be rotated along the curve of the sphere, to another point on the same sphere) I needed to convert to spherical coordinates? Rotation is based on the formulas of rotation and degree of rotation. Rotation. This calculator will tell you it's (0,-1) when you rotate by +90 deg and (0,1) when rotated by -90 deg. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the angular velocity of this rotation, or rate of change of the heading angle when the aircraft is horizontal. . We rotate this vector anticlockwise around the origin by \(\beta\) degrees. 2. In general, rotation can be done in two common directions, clockwise and anti-clockwise or counter-clockwise direction. The next lesson will discuss a few examples related to translation . 90 Degree Clockwise Rotation. Specify the angle of rotation. Here you can drag the pin and try different shapes: Angle of rotation = {eq}m \cdot \frac{360}{n} {/eq}, where m is the number of divisions between starting and ending points, and n is the total number of divisions or slices in a circle. The point of rotation can be inside or outside of the figure. The 3D rotation is different from 2D rotation. In short, switch x and y and make x negative. =sr. A rotation is different from other types of motions: translations, which have no fixed points, and reflections, each of them having an entire -dimensional fla Rotate the these four points 60 The rotation formula tells us about the rotation of a point with respect to the origin. The point is, that you're shifting the coordinate system, not the point. The angle of rotation is often measured by using a unit called the radian. The general rule for a rotation by 90 about the origin is (A,B) (-B, A) Rotation by 180 about the origin: R (origin, 180) A rotation by 180 about the origin can be seen in the picture below in which A is rotated to its image A'. (a,b) represents the point, while (x,y) represents the origin given. sin(/2) = v/(2*r) r = v/(2*sin(/2)) where: r = scalar distance of P from both A and B; v = scalar distance of B from A Then we can create a rotation matrix T = [ cos sin sin cos ] where is the counter-clockwise rotation angle. (. A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. This is the case of rotating a sprite around an arbitrary point. You will recall the following from our studies of transformations: 1. The angle of rotation is the arc length divided by the radius of curvature. A rotation is a type of rigid transformation, which means that the size and shape of the figure does not change; the figures are congruent before and after the transformation. Set up the formula for rotating a shape 180 degrees. Rotation is the field of mathematics and physics. Rotation "Rotation" means turning around a center: The distance from the center to any point on the shape stays the same. We know the points A and B and the angle at P which is theta. angle = (angle ) * (Math.PI/180); // Convert to radians var rotatedX = Math.cos (angle) * (point.x - center.x) - Math.sin (angle) * (point.y-center.y) + center.x; var rotatedY = Math.sin (angle) * (point.x - center.x) + Math.cos (angle) * (point.y - center.y) + center.y; return new createjs.Point (rotatedX,rotatedY); (Eq 3) = d d t, u n i t s ( r a d s) All particles will have the same angular velocity, with the exception of particle on the fixed axis. Formula: X = x + tx Y = y + ty where tx and ty are translation coordinates The OpenGL function is glTranslatef( tx, ty, tz ); 2. An Example 3 10 1 3 [P1]= 5 6 1 5 0 0 0 0 1 1 1 1 Given the point matrix (four points) on the right; and a line, NM, with point N at (6, -2, 0) and point M at (12, 8, 0). If you want to rotate a shape 180 degrees around the point of origin, turn the x and y coordinates into -y and -x coordinates. For Example - Let us assume, The initial coordinates of an object = (x 0, y 0, z 0) The Initial angle from origin = . Find. The 180-degree rotation is a transformation that returns a flipped version of the point or figures horizontally. The point also defines the vector \((x_1, y_1)\). Translate so that rotation axis passes through origin. The vector \((x_1, y_1)\) has length \(L\). Mouse over the application to your right to see how the centred sprite follows the mouse cursor. Below are two examples. Every point makes a circle around the center: Here a triangle is rotated around the point marked with a "+" Try It Yourself.

The fixed point is called the center of rotation . (x', y'), will be given by: x = x'cos - y'sin.

These rotations are called precession, nutation, and intrinsic rotation.

The X,Y equations listed are for CW rotations but the calculator tells you to define CCW as positive. In the general case, rotation about an arbitrary axis is more complicated. A point (a, b) rotated around the origin 270 degrees will transform to point (b - y + x, - (a - x) + y). The amount of rotation is called the angle of rotation and it is measured in degrees. What is the formula for angle of rotation? Then P' is obtained by rotating P by 90 degrees with center O = (0,0). If an object is rotated around the centre point, the object appears exactly the same as before the rotation. Let the axes be rotated about origin by an angle in the anticlockwise direction. Formula for rotating a vector in 2D Let's say we have a point \((x_1, y_1)\). 3. Common rotation angles are \(90^{0}\), \(180^{0}\) and \(270^{0}\) degrees. With rotational symmetry, a shape can be rotated (turned) and still look the same Angle of Rotation Calculator Calculator "Excellent Free Online Calculators for Personal and Business use 33r/s2 During the support phase of walking, the absolute angle of the thigh has the following angular velocities: Calculate the angular acceleration at frame 40 To rotate around the y axis by 5 degrees . The rule given below can be used to do a clockwise rotation of 270 degree. If a point is rotating 90 degrees clockwise about the origin our point M(x,y) becomes M'(y,-x).

The Right Way Equations 1 and 2 show the right way to rotate a point around the origin: x1 = x0 cos ( ) - y0 sin ( ) (Equation 1) y1 = x0 sin ( ) + y0 cos ( ) (Equation 2) If we plug in our example point of ( x0, y0) = (4, 3) and = 30, we get the answer ( x1, y1) = (1.964, 4.598), the same as before. If you use that formula with 0.707 for x and y you will find its roughly 1.0. Rotation about the x-axis by an angle x, counterclockwise (looking along the x-axis towards the origin). There is a definite center point in the rotation, and everything else revolves around that point. High School Physics Chapter 6 Section 1 It is a mechanical angle rather than an aerodynamic angle: In the absence of induced flow and/or aircraft airspeed, angle of attack and angle of incidence are the same Threads: 9 en "Angle of rotation ", angle through which the sample is turned about its mean vertical from any arbitrarily established position . Does rotate around the origin mean around 0 0? Rotate so that the rotation axis is aligned with one of the principle coordinate axes. I want to make a robot rotate around a point of origin in 2D space using data from the Teleporter service. double x1 = point.x - center.x; double y1 = point.y - center.y; double x2 = x1 * Math.cos (angle) - y1 * Math.sin (angle)); double y2 = x1 * Math.sin (angle) + y1 * Math.cos (angle)); point.x = x2 + center.x; point.y = y2 + center.y; This approach uses rotation matrices. =sr. So, the 180-degree rotation about the origin in both directions is the same and we make both h and k negative. Draw P' on your graph paper. conclude with the desired result of 3D rotation around a major axis. If you wanted to rotate that point around the origin, the coordinates of the new point would be located at (x',y'). nfries88 . Cancel Save. (. Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. The point is, that you're shifting the coordinate system, not the point. In mathematics, rotation is a transformation that revolves around a figure around a fixed point called the center of rotation. Then P0= R xPwhere the rotation matrix, R x,is given by: R x= 2 6 6 4 1 0 0 . In this lesson we'll look at how the rotation of a figure in a coordinate plane determines where it's located. A translation amongst x and y can be defined as: T ( x, y) = [ 1 0 x 0 1 y 0 0 1] As I understand, the rotation matrix around an arbitrary point, can be expressed as moving the rotation point to the origin, rotating around the origin and moving back to the original position. You may need to tap the screen to focus the mouse. To find angular velocity you would take the derivative of angular displacement in respect to time. Let P (x, y) be a point on the XY plane. Rotation: Rotation refers to rotating a point. This means that we a figure is rotated in a 180 . Cartesian and spherical coordinates are two ways of representing exactly the same Calculating Rotation Point. Find; Find and; Substitute and into and; Substitute the expression for and into in the given equation, and then simplify. Translate X to Y, so Y becomes the new origin. A rotation is a type of transformation that moves a figure around a central rotation point, called the point of rotation. Usually, you will be asked to rotate a shape around the origin, which is the point (0, 0) on a coordinate plane. When the point M (h, k) is rotating through 180, about the origin in a Counterclockwise or clockwise direction, then it takes the new position of the point M' (-h, -k). 3. R = [ cos ( ) sin ( ) 0 sin ( ) cos ( ) 0 0 0 1] with the angle and the rotation being counter-clockwise. This math worksheet was created on 2015-02-25 and has been viewed 2 times this week and 13 times this month. You can rotate shapes 90, 180, or 270 degrees around the origin using three basic formulas. To put it another way, rotation is the motion of a rigid body around a fixed point. Specify the start point and endpoint of the axis about which the objects are to be rotated (2 and 3). It is based on rotation or motion of objects around the centre of the axis. Geometry of rotation. Consider a point A rotated about the center C. Step 1: We change A to A1=A-C Step 2: We apply the rule for rotation of point A1 about origin to get A2 (a) 90 anticlockwise (x,y)-> (-y,x) (b . around a point. Completing the proof. The idea is to have an sprite "orbiting" around another sprite . Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. However, during the development of Muster my Monsters I need to perform rotations around arbitrary points. Rotating a shape 180 about the origin Squares up become squares down In 3D Rotation we also have to define the angle of Rotation with the axis of Rotation. x = x cos y sin y = y cos + x sin Where is the angle of rotation Rotating about a point in 2-dimensional space Maths Geometry rotation transformation Imagine a point located at (x,y). ( 2 votes) Cesare Fusari 7 years ago I'm a bit confused. So, if a line has the coordinates 2,4 and 4,5, it would rotate to -4,-2 and -5,-4. The above formula will rotate the point around the origin. Rotation is a circular motion around the particular axis of rotation or point of rotation. The rotation formula is used to find the position of the point after rotation. For example, (2,5) becomes (5,2). be the corresponding point after a rotation around one of the coordinate axis has been applied. These matrices are left-side multiplicated with vector positions, so the order of multiplication is from right to left - on the right side is the first operation, on the . This material shows an algebraic method to find the rotation (90, 180, 270 anticlockwise) of a point A about any point C which is not the origin. The angle of rotation is the arc length divided by the radius of curvature. In this example, we rotate a jet sprite to face the position of the mouse. Use a protractor to measure the specified angle counterclockwise. When points A, B, C are on a line, the ratio AC/AB is taken to be a signed ratio, which is negative is A is between B and C. Formula for rotation of a point by 90 degrees (counter-clockwise) Draw on graph paper the point P with coordinates (3,4). . The angle of rotation is often measured by using a unit called the radian. The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-clockwise) direction Rotation Matrices via Euler Parameters Euler Parameters where the axis of rotation is a unit vector, , and the angle of rotation about that axis is, Calculate the relative angle at the knee and the absolute angles of the . The x component of the point remains the same. Understand how we can derive a formula for the rotation of any point around the origin. Given a translation (specified by a 2D vector) and a rotation (specified by a scalar angle in radians) how do we calculate the rotation point P ? To Rotate a 3D Object Around an Axis Click Home tab > Modify panel > Rotate 3D. So you don't actually shift the point to the origin, you shift the origin to the point, and then back. Here you can drag the pin and try different shapes: The size and form of the item and its . In the figure above, the wind rotates the blades of a windmill. Geometry - Transformation - Rotation not around originHow do you rotate a shape around a point other than the origin?This geometry video explores the rotatin. These matrices are left-side multiplicated with vector positions, so the order of multiplication is from right to left - on the right side is the first operation, on the . Completing the proof If you're seeing this message, it means we're having trouble loading external resources on our website. The rotated vector has coordinates \((x_2, y_2)\) On the right, a parallelogram rotates around the red dot. I was under the impression that in order to rotate on a sphere (IE, for the point to be rotated along the curve of the sphere, to another point on the same sphere) I needed to convert to spherical coordinates? Rotation is based on the formulas of rotation and degree of rotation. Rotation. This calculator will tell you it's (0,-1) when you rotate by +90 deg and (0,1) when rotated by -90 deg. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the angular velocity of this rotation, or rate of change of the heading angle when the aircraft is horizontal. . We rotate this vector anticlockwise around the origin by \(\beta\) degrees. 2. In general, rotation can be done in two common directions, clockwise and anti-clockwise or counter-clockwise direction. The next lesson will discuss a few examples related to translation . 90 Degree Clockwise Rotation. Specify the angle of rotation. Here you can drag the pin and try different shapes: Angle of rotation = {eq}m \cdot \frac{360}{n} {/eq}, where m is the number of divisions between starting and ending points, and n is the total number of divisions or slices in a circle. The point of rotation can be inside or outside of the figure. The 3D rotation is different from 2D rotation. In short, switch x and y and make x negative. =sr. A rotation is different from other types of motions: translations, which have no fixed points, and reflections, each of them having an entire -dimensional fla Rotate the these four points 60 The rotation formula tells us about the rotation of a point with respect to the origin. The point is, that you're shifting the coordinate system, not the point. The angle of rotation is often measured by using a unit called the radian. The general rule for a rotation by 90 about the origin is (A,B) (-B, A) Rotation by 180 about the origin: R (origin, 180) A rotation by 180 about the origin can be seen in the picture below in which A is rotated to its image A'. (a,b) represents the point, while (x,y) represents the origin given. sin(/2) = v/(2*r) r = v/(2*sin(/2)) where: r = scalar distance of P from both A and B; v = scalar distance of B from A Then we can create a rotation matrix T = [ cos sin sin cos ] where is the counter-clockwise rotation angle. (. A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. This is the case of rotating a sprite around an arbitrary point. You will recall the following from our studies of transformations: 1. The angle of rotation is the arc length divided by the radius of curvature. A rotation is a type of rigid transformation, which means that the size and shape of the figure does not change; the figures are congruent before and after the transformation. Set up the formula for rotating a shape 180 degrees. Rotation is the field of mathematics and physics. Rotation "Rotation" means turning around a center: The distance from the center to any point on the shape stays the same. We know the points A and B and the angle at P which is theta. angle = (angle ) * (Math.PI/180); // Convert to radians var rotatedX = Math.cos (angle) * (point.x - center.x) - Math.sin (angle) * (point.y-center.y) + center.x; var rotatedY = Math.sin (angle) * (point.x - center.x) + Math.cos (angle) * (point.y - center.y) + center.y; return new createjs.Point (rotatedX,rotatedY); (Eq 3) = d d t, u n i t s ( r a d s) All particles will have the same angular velocity, with the exception of particle on the fixed axis. Formula: X = x + tx Y = y + ty where tx and ty are translation coordinates The OpenGL function is glTranslatef( tx, ty, tz ); 2. An Example 3 10 1 3 [P1]= 5 6 1 5 0 0 0 0 1 1 1 1 Given the point matrix (four points) on the right; and a line, NM, with point N at (6, -2, 0) and point M at (12, 8, 0). If you want to rotate a shape 180 degrees around the point of origin, turn the x and y coordinates into -y and -x coordinates. For Example - Let us assume, The initial coordinates of an object = (x 0, y 0, z 0) The Initial angle from origin = . Find. The 180-degree rotation is a transformation that returns a flipped version of the point or figures horizontally. The point also defines the vector \((x_1, y_1)\). Translate so that rotation axis passes through origin. The vector \((x_1, y_1)\) has length \(L\). Mouse over the application to your right to see how the centred sprite follows the mouse cursor. Below are two examples. Every point makes a circle around the center: Here a triangle is rotated around the point marked with a "+" Try It Yourself.

The fixed point is called the center of rotation . (x', y'), will be given by: x = x'cos - y'sin.

These rotations are called precession, nutation, and intrinsic rotation.

The X,Y equations listed are for CW rotations but the calculator tells you to define CCW as positive. In the general case, rotation about an arbitrary axis is more complicated. A point (a, b) rotated around the origin 270 degrees will transform to point (b - y + x, - (a - x) + y). The amount of rotation is called the angle of rotation and it is measured in degrees. What is the formula for angle of rotation? Then P' is obtained by rotating P by 90 degrees with center O = (0,0). If an object is rotated around the centre point, the object appears exactly the same as before the rotation. Let the axes be rotated about origin by an angle in the anticlockwise direction. Formula for rotating a vector in 2D Let's say we have a point \((x_1, y_1)\). 3. Common rotation angles are \(90^{0}\), \(180^{0}\) and \(270^{0}\) degrees. With rotational symmetry, a shape can be rotated (turned) and still look the same Angle of Rotation Calculator Calculator "Excellent Free Online Calculators for Personal and Business use 33r/s2 During the support phase of walking, the absolute angle of the thigh has the following angular velocities: Calculate the angular acceleration at frame 40 To rotate around the y axis by 5 degrees . The rule given below can be used to do a clockwise rotation of 270 degree. If a point is rotating 90 degrees clockwise about the origin our point M(x,y) becomes M'(y,-x).