Question

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 1

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

 $\left[\begin{array}{ccc}k&0\\0&k\end{array}\right]$

* 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 $\left[\begin{array}{cc}2&0\\0&2\end{array}\right]$

∵ The matrix of the vertices of the quadrilateral is

  $\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right]$

∴ The image of the quadrilateral is :

  $\left[\begin{array}{cc}2&0\\0&2\end{array}\right]\left[\begin{array}{cccc}-1&2&2&-1\\2&4&-1&-3\end{array}\right]=$

  $\left[\begin{array}{cccc}(2)(-1)+(0)(2)&(2)(2)+(0)(4)&(2)(2)+(0)(-1)&(2)(-1)+(0)(-3)\\(0)(-1)+(2)(2)&(0)(2)+(2)(4)&(0)(2)+(2)(-1)&(0)(-1)+(2)(-3)\end{array}\right]=$

 $\left[\begin{array}{cccc}-2&4&4&-2\\4&8&-2&-6\end{array}\right]$

∴ 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)