Question

Point q has coordinates -5,-4 . If you rotate q 90 degrees about the​ origin, (0,0), what are the coordinates of q​? How could you rotate q to get back to q​? Use pencil and paper. Give two other ways to rotate to get to q

Answer 1

To rotate point q(-5,-4) 90 degrees counterclockwise about the origin (0,0), the new coordinates are (4, -5). To rotate q back to q, you can rotate it 180 degrees, resulting in (-4, 5). Two other ways to rotate q to get back to q are rotating it 360 degrees or 0 degrees.

Step-by-step explanation:

To rotate a point 90 degrees counterclockwise about the origin (0,0), we can use the rotation matrix:

[cos(90°) -sin(90°)]
[sin(90°) cos(90°)]

Applying this matrix to the coordinates of point q (-5,-4), we get:

[-4 -(-5)]
[(-5) -(-4)]

Simplifying, the new coordinates are (4, -5).

To rotate q back to q, we can rotate it 180 degrees, which means using the rotation matrix:

[-1 0]
[0 -1]

Applying this matrix to the coordinates of point q (4, -5), we get:

[-4 -(-5)]
[(-5) -(-5)]

Simplifying, the new coordinates are (-4, 5).

Two other ways to rotate q to get back to q are:
1. Rotate it 360 degrees, which will bring it back to the same position: (using the rotation matrix [-1 0] [0 -1])
2. Rotate it 0 degrees, as it is already at the same position.