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)
To rotate a point (x, y) 90° clockwise, we can use the formula:
(x', y') = (y, -x)
Let's apply this formula to the endpoints of the line segment:
Endpoint 1: (0, -3)
Rotated Endpoint 1: (y, -x) = (-3, 0)
So, one endpoint of the rotated segment is (-3, 0).
Endpoint 2: (0, -7)
Rotated Endpoint 2: (y, -x) = (-7, 0)
So, another endpoint of the rotated segment is (-7, 0).
To rotate a point clockwise by 90°, you can use the following matrix transformation:
```
Rotated_x = -y
Rotated_y = x
```
Let's apply this transformation to the given endpoint (0,-7):
```
Rotated_x = -(-7) = 7
Rotated_y = 0
```
Therefore, the endpoint of the rotated line segment is (7, 0).