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?
Question: Do I start by using the rules of rotation?
90 degrees clockwise (x,y) = (y,-x)
Yes, you can start by using the rules of rotation. By applying the formula for a 90° clockwise rotation, the endpoint (0,-3) will become (-3, 0).
What to they mean with what is an endpoint of this rotated segment? I do not understand the question. Thank you.
Apologies for the confusion. "What is an endpoint of this rotated segment?" refers to finding the coordinate(s) of one of the endpoints of the line segment after it has been rotated 90° clockwise. In this case, the original line segment has endpoints (0, -3) and (0, -7). So, after rotating the line segment 90° clockwise, one of the endpoints (either (0, -3) or (0, -7)) will have a new coordinate. The question is asking for the coordinate of this new endpoint.
So, the new coordinates are (3,0) and (7,0) Correct? Thank you.
Not quite. The original endpoints of the line segment (0,-3) and (0,-7) are rotated 90° clockwise. Using the formula for a 90° clockwise rotation, the new coordinates for these endpoints would be:
(0,-3) --> (-3,0) ( x' = y, y' = -x )
(0,-7) --> (-7,0)
So the new endpoints after rotating the line segment 90° clockwise are (-3,0) and (-7,0).