Use matrices to determine the coordinates of the vertices of the reflected figure. then graph the pre-image and the image on the same coordinate grid. (picture below)

The coordinates of the vertices of the reflected figure are :

R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3) ⇒the right answer is figure (d)

Step-by-step explanation:

* Lets study the matrices of the reflection

- The matrix of the reflection across the x-axis is

- Because when we reflect any point across the x-axis we

 change the sign of the y-coordinate

- The matrix of the reflection across the y-axis is

- Because when we reflect any point across the y-axis we

 change the sign of the x-coordinate

* Now lets solve the problem

- We will multiply the matrix of the reflection across the y-axis

 by each point to find the image of each point

- The dimension of the matrix of the reflection across the y-axis

 is 2×2 and the dimension of the matrix of each point is 2×1,

then the dimension of the matrix of each image is 2×1

∵ Point R is (-3 , 7)

∴ R' =

∴ R' is (3 , 7)

∵ Point S is (7 , 2)

∴ S' =

∴ S' is (-7 , 2)

∵ Point T is (5 , -3)

∴ T' =

∴ T' is (-5 , -3)

* Look to the answer and find the correct figure

- In figure (d) R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3)

∴ The right answer is figure (d)

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true