![]() Figure 8.5.5: Relationship between the old and new coordinate planes. ![]() We may write the new unit vectors in terms of the original ones. The angle is known as the angle of rotation (Figure 8.5.5 ). Rotation 270° about the origin: Each x value becomes opposite of what it was. The rotated coordinate axes have unit vectors i and j. Introduction In this article we will practice the art of rotating shapes. We want to find the image A of the point A ( 3, 4) under a rotation by 90 about the origin. Rotations Rotating shapes about the origin by multiples of 90 Google Classroom Learn how to draw the image of a given shape under a given rotation about the origin by any multiple of 90. Rotation 180° about the origin: Each x and y value becomes opposite of what it was. Part 1: Rotating points by 90, 180, and 90. Rotation 90° about the origin: Each y-value becomes opposite of what it was. For example, 30 degrees is 1/3 of a right angle. Counterclockwise rotations have positive angles, while clockwise rotations have negative angles. Reflection across the line y=x: The x and y values switch places. To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. Reflection across the y-axis: Each y-value stays the same and each y-value becomes opposite of what it was. Reflection across the x-axis: Each x-value stays the same and each y-value becomes opposite of what it was. Transformation Rules on the Coordinate Plane Translation: Each point moves a units in the x-direction and b units in the y-direction.
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