If a with coordinates (4, -3) is rotated 90° clockwise, then rotated 180°, what are the coordinates of P"?

First, let's understand what happens to a point when it is rotated around the origin:

1. 90° clockwise rotation: The point (x, y) becomes (y, -x)
2. 180° rotation: The point (x, y) becomes (-x, -y)

Now, let's apply these transformations to the point P(4, -3):

1. After a 90° clockwise rotation, P becomes P'( -3, -4).
2. Then, after a 180° rotation, P' becomes P" (3, 4).

So, the coordinates of P" after these rotations are (3, 4).

To solve this problem, we need to understand how rotation affects coordinates in a 2D plane.

1. 90° Clockwise Rotation: The rule for a 90° clockwise rotation is (x, y) -> (y, -x). Applying this rule to point P with coordinates (4, -3), we get (-3, -4).

2. 180° Rotation: The rule for a 180° rotation is (x, y) -> (-x, -y). Applying this rule to the new coordinates (-3, -4), we get (3, 4).

So, after a 90° clockwise rotation followed by a 180° rotation, the coordinates of point P" would be (3, 4).