Chapter 11.7, Problem 20HP

To determine

To find:Draw a triangle on grid paper and its image.

Explanation of Solution

Given information:

We need to draw image of the triangle after it is moved $5$ units right and then dilated by a scale factor of $\frac{1}{3}$ .

Let us take Vertices of the triangle are

  $\begin{array}{l}A=\left(4,4\right)\\ B=\left(4,-2\right)\\ C=\left(-2,4\right)\end{array}$

When it is moved $5$ units to the right , add $5$ to each coordinate point and then since it has a scale factor of $\frac{1}{3}$ , multiply it to this fraction to get the dilated Triangle.

Vertices of Dilated Triangle are

  $\begin{array}{l}A=\left(4,4\right)\to A\text{'}\left(\frac{1}{3}\left(4+5\right),\frac{1}{3}\left(4+5\right)\right)\\ \Rightarrow A=\left(4,4\right)\to A\text{'}\left(\frac{1}{3}\left(9\right),\frac{1}{3}\left(9\right)\right)\\ \Rightarrow A=\left(4,4\right)\to A\text{'}\left(3,3\right)\end{array}$

  $\begin{array}{l}B=\left(4,-2\right)\to B\text{'}\left(\frac{1}{3}\left(4+5\right),\frac{1}{3}\left(-2+5\right)\right)\\ \Rightarrow B=\left(4,-2\right)\to B\text{'}\left(\frac{1}{3}\left(9\right),\frac{1}{3}\left(3\right)\right)\\ \Rightarrow B=\left(4,-2\right)\to B\text{'}\left(3,1\right)\end{array}$

  $\begin{array}{l}C=\left(-2,4\right)\to C\text{'}\left(\frac{1}{3}\left(-2+5\right),\frac{1}{3}\left(4+5\right)\right)\\ \Rightarrow C=\left(-2,4\right)\to C\text{'}\left(\frac{1}{3}\left(3\right),\frac{1}{3}\left(9\right)\right)\\ \Rightarrow C=\left(-2,4\right)\to C\text{'}\left(1,3\right)\end{array}$

Vertices of Dilated Triangle are

  $\begin{array}{l}A\text{'}=\left(3,3\right)\\ B\text{'}=\left(3,1\right)\\ C\text{'}=\left(1,3\right)\end{array}$

Graph of Dilated triangle is