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?
Oops, I apologize for the mistake. Yes, the correct endpoint of the rotated segment is indeed (0, 7). Thank you for catching that error.
To rotate a point 90° clockwise around the origin, we can use the formula:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
Where θ is the angle of rotation. In this case, the angle of rotation is 90°.
Let's apply this formula to rotate the endpoint (0, -7):
x' = 0*cos(90°) - (-7)*sin(90°) = 0 + 7 = 7
y' = 0*sin(90°) + (-7)*cos(90°) = 0 + 0 = 0
Therefore, the endpoint of the rotated segment is (7, 0).