91Ó°ÊÓ

An ordered pair $\left(x,y\right)$is represented by a column matrix $\left[\begin{array}{c}x\\ y\\ \end{array}\right]$which is known as vertex matrix of an ordered pair

Since, a quadrilateral has 4 ordered pair on vertices so required matrix has 2 rows and 4 columns.

First row represent $x-\text{coordinate}$ and second row represents $y-\text{coordinate}$ of each vertex.

As coordinates of the vertices of quadrilateral are $\left(-2,-2\right),\left(-6,-2\right),\left(-8,5\right),\text{and}D\left(-4,-5\right)$

Write each ordered pair as a column of a matrix to get

As perimeter is reduced to three-fourth of original quadrilateral, so vertex matrix of image is formed after dilation.

Vertex matrix after dilation is product of scale factor with given vertex matrix as shown below

$\frac{3}{4}×\left[\begin{array}{cccc}−2& −6& −8& −4\\ −2& −2& −5& −5\end{array}\right]=\left[\begin{array}{cccc}−\frac{3}{2}& −\frac{9}{2}& −6& −3\\ −\frac{3}{2}& −\frac{3}{2}& −\frac{15}{4}& −\frac{15}{4}\end{array}\right]$

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate.

Thus, coordinates of image after dilation are

$\left(−\frac{3}{2},−\frac{3}{2}\right),\left(−\frac{9}{2},−\frac{3}{2}\right),\left(−6,−\frac{15}{4}\right),\text{and}\left(−3,−\frac{15}{4}\right)$