Q3. - 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.

3. Graph $\mathbf{ABCD}$ and $\mathbf{A}\mathbf{\text{'}}\mathbf{B}\mathbf{\text{'}}\mathbf{C}\mathbf{\text{'}}\mathbf{D}\mathbf{\text{'}}$.

Step-by-Step Solution

Answer

The graph of $\mathbf{ABCD}$ and $\mathbf{A}\mathbf{\text{'}}\mathbf{B}\mathbf{\text{'}}\mathbf{C}\mathbf{\text{'}}\mathbf{D}\mathbf{\text{'}}$ is:

Step 1 ­- Description of step.

The vertex matrix for the square $ABCD$ is given by:$\left[\begin{array}{cccc}1& 4& 1& -2\\ 2& -1& -4& -1\end{array}\right]$

The vertex matrix for the square \[A'B'C'D'\] is given by:$\left[\begin{array}{cccc}-1& -4& -1& 2\\ 2& -1& -4& -1\end{array}\right]$

Step 2 ­- Description of step.

The coordinates of the square $ABCD$ are: $A\left(1,2\right)$, $B\left(4,-1\right)$, $C\left(1,-4\right)$ and $D\left(-2,-1\right)$.

The coordinates of the square $A\text{'}B\text{'}C\text{'}D\text{'}$ are: $A\text{'}\left(-1,2\right)$, $B\text{'}\left(-4,-1\right)$, $C\text{'}\left(-1,-4\right)$ and $D\text{'}\left(2,-1\right)$.

Step 3 ­- Description of step.

The graph of $ABCD$ and $A\text{'}B\text{'}C\text{'}D\text{'}$ is: