What is the rule for finding coordinates after a 90 degree rotation?
after a 180 degree rotation? after a 270 degree rotation?
Assume a circle with a radius of i(r=1)
@ 0 Degrees: = 1, and Y = 0.
@ 90 Degrees: X = 0, and Y = 1.
@ 180 Degrees: X = -1, and Y = 0.
@ 270 Degrees: X = 0, and Y = -1.
To find the coordinates after a rotation of a point by 90 degrees, 180 degrees, or 270 degrees, you can use the following rules:
1. 90 Degree Rotation:
To rotate a point (x, y) by 90 degrees counterclockwise, the new coordinates are (-y, x).
For example, let's say you have a point A with coordinates (2, 1). To rotate it by 90 degrees counterclockwise, you swap the x-coordinate with the negation of the y-coordinate, which gives us (-1, 2).
2. 180 Degree Rotation:
To rotate a point (x, y) by 180 degrees, the new coordinates are (-x, -y).
Continuing with the previous example, to rotate point A by 180 degrees, you simply negate both the x and y coordinates, resulting in (-2, -1).
3. 270 Degree Rotation:
To rotate a point (x, y) by 270 degrees counterclockwise, the new coordinates are (y, -x).
Similarly, using the previous example, to rotate point A by 270 degrees counterclockwise, you swap the x-coordinate with the negation of the y-coordinate, resulting in (1, -2).
Using these rules, you can find the coordinates after rotating a point by 90, 180, or 270 degrees. Simply follow the appropriate rule based on the desired rotation angle and apply it to the original coordinates.