Q1. - Algebra 2

Question

For Exercises 1-3, reflect square $\mathbf{ABCD}$ with vertices $\mathbf{A}\left(\mathbf{1}\mathbf{,}\mathbf{2}\right)$, $\mathbf{B}\left(\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{1}\right)$, $\mathbf{C}\left(\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{4}\right)$ and $\mathbf{D}\left(\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{1}\right)$ over the y-axis.

1. Write the coordinates in a vertex matrix.

Step-by-Step Solution

Answer

The coordinates in a vertex matrix is:

$\left[\begin{array}{cccc}\mathbf{1}& \mathbf{4}& \mathbf{1}& \mathbf{-}\mathbf{2}\\ \mathbf{2}& \mathbf{-}\mathbf{1}& \mathbf{-}\mathbf{4}& \mathbf{-}\mathbf{1}\\ & & & \end{array}\right]$

Step 1 ­- Description of step.

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

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

.

Step 2 ­- Description of step.

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

Step 3 ­- Description of step.

The vertex matrix for the square \[ABCD\] is given by:

$\left[\begin{array}{cccc}1& 4& 1& -2\\ 2& -1& -4& -1\\ & & & \end{array}\right]$