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. (0, 3)
2. (3, 0)
3. (0, 7)
4. (-3, 0)
To rotate a point (x, y) 90° clockwise, we can use the following formula:
(x', y') = (-y, x)
Let's apply this formula to the given endpoints of the line segment:
For the first endpoint (0, -3):
(-y, x) = (-(-3), 0) = (3, 0)
For the second endpoint (0, -7):
(-y, x) = (-(-7), 0) = (7, 0)
Therefore, the rotated segment has endpoints (3, 0) and (7, 0).
The correct answer is option 2: (3, 0)
Rotate a point on a line at (-4, 6) 180° counterclockwise. What is the resulting point? (1 point)
(4,6)
(-6, 4)
(6,4)
(-4,6)