Quick ❗️❗️ which sequence of transformations will change did your pqrs to figure p’q’r’s’?
a. counterclockwise rotation about the origin by 90° followed by reflection over the x-axis
b. counter clockwise rotation about the origin by 180° followed by reflection over the x- axis
c. counterclockwise rotation about the origin by 180° followed by reflection over the y-axis
d. counterclockwise rotation about the origin by 90° followed by reflection over the y-axis

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

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9