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??
To rotate a line segment 90° clockwise, we can use the following transformation matrix:
[x'] [0 -1] [x]
[y'] = [1 0] [y]
Let's apply this matrix to the given line segment with endpoints (0,-3) and (0,-7):
Endpoint (0,-3):
x = 0
y = -3
[x'] [0 -1] [0] [0]
[y'] = [1 0] [-3] [3]
Calculating the matrix multiplication:
x' = (0)(0) + (-1)(-3) = 3
y' = (1)(0) + (0)(-3) = 0
So, the endpoint (0,-3) after rotating 90° clockwise is (3,0).
Endpoint (0,-7):
x = 0
y = -7
[x'] [0 -1] [0] [0]
[y'] = [1 0] [-7] [7]
Calculating the matrix multiplication:
x' = (0)(0) + (-1)(-7) = -7
y' = (1)(0) + (0)(-7) = 0
So, the endpoint (0,-7) after rotating 90° clockwise is (-7,0).
Therefore, an endpoint of the rotated segment is (-7,0).
wrong
Apologies for the mistake in my previous response.
To rotate a point (x, y) by 90° clockwise, we can use the following formulas:
x' = y
y' = -x
Endpoint (0, -3):
x = 0
y = -3
Applying the formulas:
x' = -3
y' = 0
Hence, the endpoint (0, -3) after rotating 90° clockwise is (-3, 0).
Endpoint (0, -7):
x = 0
y = -7
Applying the formulas:
x' = -7
y' = 0
Therefore, the endpoint (0, -7) after rotating 90° clockwise is (-7, 0).
Hence, an endpoint of the rotated segment is (-7, 0).