Graph Quadrilateral ABCD whose vertex matrix is shown below. Then graph the dilation of Quadrilateral ABCD with a scale factor of 3 on the same coordinate grid.

Answer:The coordinates of the vertices of the dilated figure are:A' is (-3 , 6), B' is (15 , 15), C' is (15 , 9), D' is (-12 , -3) ⇒ the answer is (a)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}{cc}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 3∴ The matrix of dilation is [tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right][/tex] ∵ The matrix of the vertices of the quadrilateral is   [tex]\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right][/tex]∴ The image of the quadrilateral is :   [tex]\left[\begin{array}{cc}3&0\\0&3\end{array}\right]\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right]=[/tex]   [tex]\left[\begin{array}{cccc}(3)(-1)+(0)(2)&(3)(5)+(0)(5)&(3)(5)+(0)(3)&(3)(-4)+(0)(-1)\\(0)(-1)+(3)(2)&(0)(5)+(3)(5)&(0)(5)+(3)(3)&(0)(-4)+(3)(-1)\end{array}\right][/tex]   [tex]\left[\begin{array}{cccc}-3&15&15&-12\\6&15&9&-3\end{array}\right][/tex]∴ The image of point A' is (-3 , 6)∴ The image of point B' is (15 , 15)∴ The image of point C' is (15 , 9)∴ The image of point D' is (-12 , -3)* The answer is figure (a)