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.

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  [tex]\left[\begin{array}{ccc}k&0\\0&k\end{array}\right][/tex]* 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 [tex]\left[\begin{array}{cc}2&0\\0&2\end{array}\right][/tex]∵ The matrix of the vertices of the quadrilateral is   [tex]\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right][/tex]∴ The image of the quadrilateral is :   [tex]\left[\begin{array}{cc}2&0\\0&2\end{array}\right]\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right]=[/tex]   [tex]\left[\begin{array}{cccc}(2)(-1)+(0)(2)&(2)(2)+(0)(4)&(2)(2)+(0)(-1)&(2)(-1)+(0)(-3)\\(0)(-1)+(2)(2)&(0)(2)+(2)(4)&(0)(2)+(2)(-1)&(0)(-1)+(2)(-3)\end{array}\right]=[/tex]  [tex]\left[\begin{array}{cccc}-2&4&4&-2\\4&8&-2&-6\end{array}\right][/tex]∴ 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)