Chapter 4.4, Problem 14PPS

To determine

To find: The coordinates of the vertices of each of the image after the given translational and then graph the image and the pre-image.

Answer to Problem 14PPS

The coordinate of the vertices is $A^{\prime }\left(-6,-1\right),B^{\prime }\left(-3,1\right),C^{\prime }\left(-2,-5\right)$ and the graph for the image and pre image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $A\left(-1,2\right),B\left(2,4\right),C\left(3,-2\right)$ .

The vertices are translated 5 units to the right and 3 units down.

Calculation:

Consider the vertices of the image are,

  $A\left(-1,2\right),B\left(2,4\right),C\left(3,-2\right)$

The vertices are translated 5 units to the right and 3 units down. Then,

  $\left[\begin{array}{ccc}-1& 2& 3\\ 2& 4& -2\end{array}\right]+\left[\begin{array}{ccc}-5& -5& -5\\ -3& -3& -3\end{array}\right]=\left[\begin{array}{ccc}-6& -3& -2\\ -1& 1& -5\end{array}\right]$

Thus, the coordinate of the vertices of the image is $A^{\prime }\left(-6,-1\right),B^{\prime }\left(-3,1\right),C^{\prime }\left(-2,-5\right)$ .

The graph for the image and the pre-image is shown in Figure 1

  

Figure 1