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)
Responses
(0, 7)
left parenthesis 0 comma 7 right parenthesis
(3, 0)
left parenthesis 3 comma 0 right parenthesis
(0, 3)
left parenthesis 0 comma 3 right parenthesis
(−3, 0)
left parenthesis negative 3 comma 0 right parenthesis
Skip to navigation
To rotate a point 90° clockwise, we can use the following formulas:
x' = x*cosθ + y*sinθ
y' = -x*sinθ + y*cosθ
In this case, since we are rotating a line segment around the origin (0, 0), the x and y coordinates of the endpoints will change as follows:
For the endpoint (0, -3):
x' = 0*cos(90°) + (-3)*sin(90°)
= 0 + (-3)
= -3
y' = (-1)*0*sin(90°) + (-3)*cos(90°)
= 0 + 3
= 3
Therefore, the new endpoint after rotating is (0, 3).
Therefore, the correct answer is:
(0, 3)
left parenthesis 0 comma 3 right parenthesis