Q18. - Algebra 2

Question

For exercises 18-20, use the following information

The vertices of $\Delta XYZ$ are $X\left(1,-1\right),Y\left(2,-4\right),\text{ and }Z\left(7,-1\right)$. The triangle is reflected over the line $y=x$

18. Write the coordinates for $\Delta XYZ$ in a vertex matrix

Step-by-Step Solution

Answer

Coordinates of triangle $XYZ$ in vertex matrix is $\left[\begin{array}{ccc}1& 2& 7\\ -1& -4& -1\\ & & \end{array}\right]$

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 triangle

Since, a triangle has 3 ordered pair on vertices so required matrix has 2 rows and 3 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 triangle are $X\left(1,-1\right),Y\left(2,-4\right),\text{ and }Z\left(7,-1\right)$ 

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

$\left[\begin{array}{ccc}1& 2& 7\\ -1& -4& -1\end{array}\right]$