Chapter 9.2, Problem 6CYU

To determine

To find: The parallelogram $WXYZ$ with vertices $W\left(-6,-5\right),X\left(-2,-5\right),Y\left(-1,-8\right)$ and $Z\left(-5,-8\right)$ ; $\left(-1,4\right)$

Answer to Problem 6CYU

The parallelogram $WXYZ$ with vertices $W\left(-6,-5\right),X\left(-2,-5\right),Y\left(-1,-8\right)$ and $Z\left(-5,-8\right)$ ; $\left(-1,4\right)$ .

Explanation of Solution

Given information:

The given parallelogram $WXYZ$ with vertices $W\left(-6,-5\right),X\left(-2,-5\right),Y\left(-1,-8\right)$ and $Z\left(-5,-8\right)$ ; $\left(-1,4\right)$ .

Calculation:

Consider the translate vector.

  $\left(x,y\right)\to \left(x+a,y+b\right)$

The vector indicates a translation of $7$ units to the right and $1$ unit up.

  $\begin{array}{c}\left(x,y\right)\to \left(x-1,y+4\right)\\ W\left(-6,-5\right)\to W\text{'}\left(-7,-1\right)\\ X\left(-2,-5\right)\to X\text{'}\left(-3,-1\right)\\ Y\left(-1,-8\right)\to Y\text{'}\left(-2,-4\right)\\ Z\left(-5,-8\right)\to Z\text{'}\left(-6,-4\right)\end{array}$

The graph coordinate point is shown in figure(1).

  

Figure (1)

Therefore the parallelogram $WXYZ$ with vertices $W\left(-6,-5\right),X\left(-2,-5\right),Y\left(-1,-8\right)$ and $Z\left(-5,-8\right)$ ; $\left(-1,4\right)$ is shown in figure (1).