Chapter 4, Problem 14STP

a.

To determine

To find the vertices of $△RST$ .

Answer to Problem 14STP

  $R=(6,4),S=(8,-6),T=(2,-2)$

Explanation of Solution

Given:

The graph is as follows.

  

Calculation:

From the figure, the vertices of the triangle are as follows.

  $R=(6,4),S=(8,-6),T=(2,-2)$

Therefore, the vertices of the triangle is $R=(6,4),S=(8,-6),T=(2,-2)$ .

b.

To determine

To write the coordinates in a vertex matrix.

Answer to Problem 14STP

  $\left(\begin{array}{cc}6& 82\\ 4& -6-2\end{array}\right)$

Explanation of Solution

The coordinates in vertex matrix are-

  $\left(\begin{array}{cc}6& 82\\ 4& -6-2\end{array}\right)$

c.

To determine

To find the matrix by which you will multiply to get the reflected vertices.

Answer to Problem 14STP

  $\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$

Explanation of Solution

Since the triangle is reflected across $y=x$ , the following matrix should be used to multiply −

  $\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$

d.

To determine

To find the vertices of the reflected matrix.

Answer to Problem 14STP

  $\left(4,6\right),\left(-6,8\right),\left(-2,2\right)$

Explanation of Solution

Reflected coordinates: $\left(4,6\right),\left(-6,8\right),\left(-2,2\right)$