Chapter 4.4, Problem 1CYP

To determine

The coordinates of the vertices of the image of triangle RST if it is moved $3$

Units to the right and $4$ units up.

Explanation of Solution

Given Information:

The coordinates of the vertices of the triangle RST is

  $\begin{array}{l}R(-1,5)\\ S(2,1)\\ T(-3,2)\end{array}$

Calculation:

Now the vertex matrix of the triangle RST is,

  $\left|\begin{array}{ccc}-1& 2& -3\\ 5& 1& 2\end{array}\right|$

Now to move the vertex $3$ Units to the right we have to add $3$ in each X coordinates and to move the vertex $4$ Units up we have to add $4$ in each Y coordinates. This can be done by adding transition matrix to vertex matrix,

The transition matrix is,

  $\left|\begin{array}{ccc}3& 3& 3\\ 4& 4& 4\end{array}\right|$

Now the required vertex matrix is,

  $\begin{array}{l}\left|\begin{array}{ccc}-1& 2& -3\\ 5& 1& 2\end{array}\right|+\left|\begin{array}{ccc}3& 3& 3\\ 4& 4& 4\end{array}\right|\\ =\left|\begin{array}{ccc}2& 5& 0\\ 9& 5& 6\end{array}\right|\end{array}$

Therefore the coordinates of the vertices of the triangle RST after moving $3$

units to the right and $4$ units up is

  $\begin{array}{l}R(2,9)\\ S(5,5)\\ T(0,6)\end{array}$

The graphs of the triangles are shown below.