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)

Question

1.(-3,0)
2.(3,0)
3.(0,3)
4.(0,7)

Answer 1

To rotate a point 90° clockwise around the origin, we can use the following rotation formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the original coordinates, (x', y') are the coordinates after rotation, and θ is the angle of rotation (in radians).

In this case, we want to rotate the line segment with endpoints (0,-3) and (0,-7) 90° clockwise. Since the x-coordinate remains the same, we only need to calculate the new y-coordinate.

For the first endpoint:
(x', y') = (0*cos(90°) - (-3)*sin(90°), 0*sin(90°) + (-3)*cos(90°))
= (0 + 3, 0 - 0)
= (3, 0)

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

So the correct answer is: 2. (3, 0)