Question

A segment with the endpoint X(-6,2) and Y(-1,-3) is rotated 90 degrees about the origin. What are the coordinates of X' and Y'?

Answer 1

Draw the two points in a rectangular coordinate system.

Draw a vector from the origin (0,0) until the point Y whose coordinates are (-1,3). Rotate the vector 90 degress anticlockwise.

You can see that the tip of the vector will fall in a point with coordinates (3,-1).

Then Y' is (3,-1).

Follow same procedure with point X(-6,2). The point of the vector will translate to X' with coordinates (-2,-6).

A 90 degrees anticlockwise rotation transforms coordinates (a,b) to  (-b,a)

Then the answer is the option 3 - X'(-2,-6) Y'( 3,-1).

By convention if there is not indication the angles must be taken anticlockwise, but it would be better to indicate it.

If you rotate 90 degress clockwise the end points would be X'(2,6) Y'(3,-1).

Answer 2

the answer is  option 3 - X'(-2,-6) Y'( 3,-1).