when you're rotating a trapezoid that's in quadrant 4 90 degrees, does the trapezoid goes in quadrant 2 and the coordiantes switch?

also, does the trapezoid goes in quadrant 1 when rotating 180 degrees

This is my answer? Is this right?

No,

if your trapezoid is in quadrant 4, then a rotation of 90ºwould put you in quadrant 1, (counterclockwise is the positive rotation in math).
Consider a possible point on the original trapezoid, lets say (5,-2)
Its image point would be (2,5)
So under a rotation of 90º any point (a,b) would have its image point (-b,a)

Similarly after a rotation of 180º, your fourth quadrant trap would land in the second quadrant, so any point (a,b) would have its image point become (-a,-b)

If you know anything about matrices, a 90º rotation has a rotation matrix of
0 -1
1 0
and a 180º rotation matrix is
-1 0
0 -1

When rotating a shape, such as a trapezoid, in the coordinate plane, the shape itself remains in the same quadrant; only the positions of its vertices change. Here's how the coordinates of the trapezoid's vertices change when rotating:

1. Rotation of 90 degrees clockwise in Quadrant 4:
- The coordinates of the original trapezoid's vertices would change as follows:
- (x, y) becomes (y, -x)
- So, the trapezoid would remain in Quadrant 4, but the coordinates would switch and flip.

2. Rotation of 180 degrees in Quadrant 4:
- The coordinates of the original trapezoid's vertices would change as follows:
- (x, y) becomes (-x, -y)
- The trapezoid would move to Quadrant 1, but its coordinates would stay the same in terms of switching.

Remember, it's important to rotate around a fixed point, known as the origin (0,0), unless otherwise stated.