Q26. - Algebra 2

Question

For exercises 26-28, use quadrilateral $QRST$ shown at the right.

26. Write the vertex matrix. Multiply the vertex matrix by $-1$

Step-by-Step Solution

Answer

Coordinates of quadrilateral $QRST$ in vertex matrix is $\left[\begin{array}{cccc}2& 4& 2& -3\\ 3& -3& -5& -2\end{array}\right]$

Multiplication of vertex matrix with $-1$ gives $\left[\begin{array}{cccc}-2& -4& -2& 3\\ -3& 3& 5& 2\end{array}\right]$

Step 1 - Vertex matrix

An ordered pair $\left(x,y\right)$ is represented by a column matrix $\left[\begin{array}{c}x\\ y\\ \end{array}\right]$ which is known as vertex matrix of an ordered pair.

Step 2 - Vertex matrix of a quadrilateral

Since, a quadrilateral has 4 ordered pair on vertices so required matrix has 2 rows and 4 columns.

First row represent $x-\text{coordinate}$ and second row represents $y-\text{coordinate}$ of each vertex.

Step 3 - Required vertex matrix

As coordinates of the vertices of quadrilateral are $Q\left(2,3\right),R\left(4,-3\right)\text{, }S\left(2,-5\right)\text{, and }T\left(-3,-2\right)$

Write each ordered pair as a column of a matrix to get

$\left[\begin{array}{cccc}2& 4& 2& -3\\ 3& -3& -5& -2\end{array}\right]$

Step 4 - Multiply with - 1

Multiply the vertex matrix of given quadrilateral with $-1$ to get

$-1\times \left[\begin{array}{cccc}2& 4& 2& -3\\ 3& -3& -5& -2\end{array}\right]=\left[\begin{array}{cccc}-2& -4& -2& 3\\ -3& 3& 5& 2\end{array}\right]$