Question

1) Point P has the coordinates (5,7) what is the image of P' after a 90-degree Rotation? 2) Point P has the coordinates (5,7) what is the image of P' after a 180-degree Rotation? 3) Point P has the coordinates (5,7) what is the image of P' after a 270-degree Rotation? 4) Point A has the coordinates (-5,7) what is the image of A' after a 90-degree Rotation? 5) Point Q has the coordinates (5,7) what is the image of Q' after a 270-degree Rotation? 6) L' (6,-7) is the image of L after a 180 rotation what are the original coordinates L 7) The point A (-5,-8) is first translated 6 units to the right and two units down to get A'.A' is then reflected in the y=-x line to get A''.A'' is then rotated counterclockwise around the origin 270 degrees to get A'''.What are the coordinates of A'''?

Answer 1

1) The coordinates of P' is (7, -5)

2) The coordinates of P' is (-5, -7)

3) The coordinates of P' is (-7, 5)

4) The coordinates of A' is (7, 5);

5) Q' is (-7, 5)

6) The coordinates of L is (-6, 7)

7) The coordinates of A''' is (1, 10)

Explanation:

1) The coordinates of a preimage (x, y) after 90-degrees clockwise rotation gives the image (y, -x)

Therefore, given that the preimage P is (5, 7), we have the image, P', after 90 degrees clockwise rotation is (7, -5);

2) The coordinates of a preimage (x, y) after 180-degrees clockwise rotation gives the image (-x, -y)

Given that the preimage, point P, has coordinates (5, 7) the image, P', after 180-degrees rotation becomes (-5, -7)

3) The coordinates of a preimage (x, y) after 270-degrees clockwise rotation gives the image (-y, x)

∴ The coordinates of the preimage, P = (5, 7), after 270-degrees clockwise rotation gives the image, P', = (-7, 5)

4) The coordinates of a preimage (x, y) after 90-degrees clockwise rotation gives the image (y, -x)

Therefore, given that the preimage A is (-5, 7), we have the image, A', after 90 degrees clockwise rotation is (7, 5);

5) The coordinate of the preimage, point Q is (5, 7) after 270-degrees clockwise rotation gives the image, Q', = (-7, 5)

6) The image of a preimage, (x, y) after 180-degrees rotation is (-x, -y). Therefore, given that the image of the preimage L, after 180 degrees rotation is L' (6, -7), we have the coordinates of L is (-6, 7)

7) The coordinates of the preimage, A = (-5, -8)

a) A is translated 6 units to the right and 2 units to give;

A'(-5 + 6, -8 - 2) = A'*1, -10)

b) (x, y) is reflected across the line y = -x, to give (-y, -x)

∴ A'(1, -10) is reflected across the line y = -x, A''(10, -1)

c) The coordinates of a preimage (x, y) after 270-degrees clockwise rotation gives the image (-y, x)

∴ The coordinates of the preimage, A''(10, -1), after 270-degrees clockwise rotation gives the image, A'''(1, 10).