Q56. - Algebra 2

Question

For exercises 56-58, use the following information

The vertices of $\Delta ABC$are $A\left(-2,1\right),B\left(1,2\right),\text{ and }C\left(2,-3\right)$. The triangle is dilated so that its perimeter is $2\frac{1}{2}$ times the original perimeter.

56. Write the coordinates for $\Delta ABC$ in a vertex matrix

Step-by-Step Solution

Answer

Coordinates of triangle $ABC$ in vertex matrix is $\left[\begin{array}{ccc}-2& 1& 2\\ 1& 2& -3\\ & & \end{array}\right]$

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 $A\left(-2,1\right),B\left(1,2\right),\text{ and }C\left(2,-3\right)$

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

 $\left[\begin{array}{ccc}-2& 1& 2\\ 1& 2& -3\\ & & \end{array}\right]$