Q36. - Algebra 2

Question

For Exercises 34-38, use the figure below.

Graph the vertices of the transformed rectangle. Describe the transformation.

Step-by-Step Solution

Answer

The graph of the vertices of the transformed rectangle is:

The transformation is a dilation in which the rectangle has becomes two times enlarged that is all the linear measures of the transformed rectangle is two times the linear measures of the given rectangle.

Step 1 ­- Observe the given figure.

The given figure is:

Step 2 ­- Description of step.

It is being given that $B=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$

The vertex matrixA is given by: $A=\left[\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\right]$

Therefore, the value of BA is given by:

$\begin{array}{c}BA=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]\cdot \left[\begin{array}{c}\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\end{array}\right]\\ =\left[\begin{array}{c}\begin{array}{cccc}0+0& 8+0& 4+0& -4+0\\ 0+0& 0+8& 0+12& 0+4\end{array}\end{array}\right]\\ =\left[\begin{array}{c}\begin{array}{cccc}0& 8& 4& -4\\ 0& 8& 12& 4\end{array}\end{array}\right]\end{array}$

Therefore , the vertex matrix for the transformed rectangle is:$BA=\left[\begin{array}{c}\begin{array}{cccc}0& 8& 4& -4\\ 0& 8& 12& 4\end{array}\end{array}\right]$

Therefore, it can be noticed that the vertices of the transformed rectangle are: $(0,0)$,$(8,8)$ ,$(4,12)$ and $(-4,4)$.

Step 3 ­- Draw the graph of the vertices of the transformed rectangle.

The graph of the vertices of the transformed rectangle is: