Q34. - Algebra 2

Question

For Exercises 34-38, use the figure below.

Write the vertex matrix for the rectangle.

Step-by-Step Solution

Answer

The vertex matrix for the rectangle is$\mathbf{A}\mathbf{=}\left[\begin{array}{c}\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\end{array}\right]$

Step 1 ­- Observe the given figure.

The given figure is:

Step 2 ­- Description of step.

From the given figure, it can be noticed that the vertices of the rectangle are:$\left(0,0\right)$, $\left(4,4\right)$, $\left(2,6\right)$ and $\left(-2,2\right)$.

The ordered pair $\left(x,y\right)$ can be represented by the column matrix.

$\left[\begin{array}{c}x\\ y\end{array}\right]$

The vertex matrix is the matrix obtained by combining all the column matrices of all the ordered points in the given figure.

Therefore, the vertex matrix of the given rectangle is the matrix obtained by combining all the column matrices of all the ordered points of the given rectangle.

Step 3 ­- Write the vertex matrix for the rectangle.

Therefore, the vertex matrix for the rectangle is$A=\left[\begin{array}{c}\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\end{array}\right]$