90 Degree Rotation Around A Point That Is Not The Origin

This video shows how to rotate a triangle 90 degrees clockwise around a point that is not the origin which involves translation of the center of rotation to the origin.

Here is how you rotate an object 90 degrees on the coordinate plane around a point that is not the origin:

1. Translate the Coordinate Plane: Suppose the point you want to rotate around is (a, b). If the coordinates of a point to be rotated are (x, y), then you subtract (a, b) from (x, y) to translate the coordinate plane:

New x-coordinate = x - a New y-coordinate = y - b

2. Perform the Rotation: For a 90-degree counterclockwise rotation around the origin, the new coordinates (x', y') of a point (x, y) after rotation are given by: x' = -y y' = x

3. Translate Back: After rotating the object, you need to translate the coordinate plane back to its original position by adding (a, b) to the coordinates of the rotated points:

New x-coordinate = x' + a New y-coordinate = y' + b

These steps ensure that the object is rotated 90 degrees counterclockwise around the specified point. Remember to apply these transformations to every point on the object you want to rotate.


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