Question

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)
Responses

Answer 1

To find the endpoint of the rotated line segment, we can use the properties of rotations.

First, let's represent the line segment with endpoints (0,-3) and (0,-7) by a vector.

The vector representing the line segment is given by:

v = (-3, -7) - (0, -3) = (-3, -4)

To rotate a vector 90° clockwise, we can use the following rotation matrix:

R = [cos(90°) -sin(90°)
sin(90°) cos(90°)]

Applying the rotation matrix to the vector, we get:

R * v = [-4, 3]

Therefore, the endpoint of the rotated line segment is (0, 3).