Demonstrating the properties of rotations, if a line segment with endpoints (0,-3) and (0,-7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment
To rotate a point (x, y) by 90 degrees clockwise, we can use the following formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Let's apply this formula to the endpoints of the line segment (0, -3) and (0, -7) being rotated by 90 degrees clockwise.
For the point (0, -3), we have:
x = 0
y = -3
Using the formula, we get:
x' = 0 * cos(90°) - (-3) * sin(90°) = 0 + 3 = 3
y' = 0 * sin(90°) + (-3) * cos(90°) = 0 - 3 = -3
Therefore, the new coordinates after rotating the point (0, -3) by 90 degrees clockwise are (3, -3).
Similarly, for the point (0, -7), we have:
x = 0
y = -7
Using the formula, we get:
x' = 0 * cos(90°) - (-7) * sin(90°) = 0 + 7 = 7
y' = 0 * sin(90°) + (-7) * cos(90°) = 0 - 7 = -7
Therefore, the new coordinates after rotating the point (0, -7) by 90 degrees clockwise are (7, -7).
Hence, an endpoint of the rotated segment is (3, -3) or (7, -7).