A segment has endpoints (−2,4)%0D%0A-%0D%0A2%0D%0A,%0D%0A4%0D%0A and (1,5)%0D%0A1%0D%0A,%0D%0A5%0D%0A . What are the endpoints after a 90°%0D%0A90%0D%0A°%0D%0A counterclockwise rotation?

Answer 1

To find the endpoints after a 90° counterclockwise rotation, we can apply the rotation matrix to each endpoint.

The rotation matrix for a counterclockwise rotation of 90° is:

[ 0 -1 ]
[ 1 0 ]

For the first endpoint (-2, 4), we can multiply the rotation matrix by the coordinates as follows:

[ 0 -1 ] [ -2 ] [ -1 ]
[ 1 0 ] [ 4 ] = [ 4 ]

Therefore, the first endpoint after the rotation is (-1, 4).

For the second endpoint (1, 5), we can multiply the rotation matrix by the coordinates as follows:

[ 0 -1 ] [ 1 ] [ -1 ]
[ 1 0 ] [ 5 ] = [ 5 ]

Therefore, the second endpoint after the rotation is (-1, 5).

So, the endpoints after a 90° counterclockwise rotation are (-1, 4) and (-1, 5).