Answer:
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)