Chapter 4.4, Problem 1CYU

To determine

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

Answer to Problem 1CYU

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

Explanation of Solution

Given:

The given vertices are $A\left(-3,-3\right),B\left(-4,2\right),C\left(1,0\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $A\left(-3,-3\right),B\left(-4,2\right),C\left(1,0\right)$

The coordinates are translated 5 units to the right and three units to the down. Then the coordinate of the vertices is,

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

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

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

  

Figure 1