Demonstrating the properties of rotations, if a line segment with endpoint (0,-3) and (0,-7) is rotated 90° clockwise, what is an endpoint of this rotated segment?
To rotate a point (x,y) 90° clockwise, we can use the following rule:
(x',y') = (y,-x)
Let's apply this rule to the endpoint (0,-7) first:
(0', -7') = (-7, -0)
= (-7, 0)
So the new coordinates for the endpoint (0,-7) after a 90° clockwise rotation are (-7,0).
Now let's apply the rule to the other endpoint (0,-3):
(0', -3') = (-3, -0)
= (-3, 0)
So the new coordinates for the endpoint (0,-3) after a 90° clockwise rotation are (-3,0).
Therefore, an endpoint of the rotated segment is (-3,0).