Rotations quick check demonstrating the properties of rotations if a line segment with endpoints 0, - 3 and 0, - 7 is rotated 90° clockwise what is the endpoint of this rotated segment minus 3, 0 0, 7 0, 3 3, 0

Answer 1

To find the endpoint of a line segment after a 90° clockwise rotation, you can apply the following transformation matrix:

[x']
[y'] = [0 -1] * [x]
[1 0]

Considering the given line segment with endpoints (0, -3) and (0, -7), let's determine the endpoint after the rotation:

For the first endpoint (0, -3):

x = 0
y = -3

By substituting these values into the transformation matrix, we get:

[x'] [0 -1] * [0] [(-1)(0) + (0)(-3)] [0]
[y'] = [1 0] * [-3] = [(0)(0) + (1)(-3)] [-3]

Therefore, the endpoint after rotation is (0, -3) -> (0, 3).

For the second endpoint (0, -7):

x = 0
y = -7

By substituting these values into the transformation matrix, we get:

[x'] [0 -1] * [0] [(-1)(0) + (0)(-7)] [0]
[y'] = [1 0] * [-7] = [(0)(0) + (1)(-7)] [-7]

Therefore, the endpoint after rotation is (0, -7) -> (0, -7).

Thus, the endpoints after the 90° clockwise rotation are (0, 3) and (0, -7).