![]() These are rigid transformations wherein the image is congruent to its pre-image. ![]() A great math tool that we use to show rotations is the coordinate grid. You can use the following rules when performing any counterclockwise rotation. ![]() For a rotation \(r_O\) of 90° centered on the origin point \(O\) of the Cartesian plane, the transformation matrix is \(\begin\). From the definition of the transformation, we have a rotation about any point, reflection over any line, and translation along any vector. Here is a figure rotated 90° clockwise and counterclockwise about a center point.The rule of a rotation \(r_O\) of 270° centered on the origin point \(O\) of the Cartesian plane in the positive direction (counter-clockwise), is \(r_O : (x, y) ↦ (y, −x)\). Rules for Rotations In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. Rotating about a point in 2-dimensional space. 'Rotation' means turning around a center: The distance from the center to any point on the shape stays the same. The rule of a rotation \(r_O\) of 180° centered on the origin point \(O\) of the Cartesian plane, in the positive direction (counter-clockwise) is \(r_O : (x, y) ↦ (−x, −y)\). Rotations are counterclockwise unless otherwise stated. ![]()
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