Answer:
Counterclockwise rotation about the origin by 90° followed by reflection over the Y-axis ⇒ answer (D)
Step-by-step explanation:
* Lets revise the reflection and the rotation of a point
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) rotated about the origin by angle 90° counter clockwise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clockwise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
- In our problem
# The vertices of the original figure are:
P(1 , -3) , Q (3 , -2) , R (3 ,-3) , S (2 , -4)
# The vertices of the image are:
P' (-3 , 1) , Q' (-2 , 3) , R' (-3 , 3) , S' (-4 , 2)
∵ x and y are switched
∴ The figure is rotated about origin by 90°
∵ The signs of the x-coordinates and the y-coordinates
didn't change
∴ The rotation is followed by reflection, to know about which
axis we must to find the images after the rotation
∵ P (1 , -3) ⇒ after rotation 90° counter clockwise is (3 , 1)
∵ Q (3 , -2) ⇒ after rotation 90° counter clockwise is (2 , 3)
∵ R (3 , -3) ⇒ after rotation 90° counter clockwise is (3 , 3)
∵ S (2 , -4) ⇒ after rotation 90° counter clockwise is (4 , 2)
* The images are P' (-3 , 1) , Q' (-2 , 3) , R' (-3 , 3) , S' (-4 , 2)
- The sign of x-coordinates of all of them changed
∴ The rotation followed by reflection over the y-axis
* The answer is ⇒ Counterclockwise rotation about the origin
by 90° followed by reflection over the Y-axis
