Demonstrating the properties of rotations, if a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, what is an endpoint of this rotated segment?(1 point) plzzzz helpppp
To rotate a point (x, y) 90° clockwise, we can use the following rotation matrix:
[ 0 -1 ]
[ 1 0 ]
Let's apply this matrix to the endpoints of the line segment (0, -3) and (0, -7):
For the first endpoint (0, -3):
x' = 0 * 0 + (-1) * (-3) = 3
y' = 1 * 0 + 0 * (-3) = 0
So the rotated endpoint is (3, 0).
For the second endpoint (0, -7):
x' = 0 * 0 + (-1) * (-7) = 7
y' = 1 * 0 + 0 * (-7) = 0
So the rotated endpoint is (7, 0).
Therefore, an endpoint of the rotated line segment is (7, 0).