Use scalar multiplication to determine the coordinates of the vertices of the dilated figure. then graph the pre-image and the image of the same coordinate grid.

The coordinates of the vertices of the dilated figure are:

A' is (-2 , 4), B' is (4 , 8), C' is (4 , -2), D' is (-2 , -6) ⇒ the answer is (d)

Step-by-step explanation:

* Lets study the matrix of the dilation

- If we dilate any point by scale factor k we  multiply the

 coordinates of the point by k

- The matrix of the dilation by scale factor k is

* Now lets solve the problem

- We will multiply the matrix of dilation by the matrix of the

  vertices of the quadrilateral

- The dimension of the matrix of the dilation is 2×2 and the

  dimension of the matrix of the vertices of the quadrilateral

  is 2×4 then the dimension of the matrix of the image of the

  quadrilateral is 2×4

∵ The scale factor is 2

∴ The matrix of dilation is

∵ The matrix of the vertices of the quadrilateral is

∴ The image of the quadrilateral is :

∴ The image of point A' is (-2 , 4)

∴ The image of point B' is (4 , 8)

∴ The image of point C' is (4 , -2)

∴ The image of point D' is (-2 , -6)

* The right answer is figure (d)

step-by-step :