Q21. - Algebra 2

Question

For exercises 21-23, use the following information

Parallelogram $DEFG$ with $D\left(2,4\right),E\left(5,4\right),F\left(4,1\right),\text{ and }G\left(1,1\right)$ is rotated $270°$ counter clockwise about the origin. 

21. Write the coordinates of the parallelogram in a vertex matrix.

Step-by-Step Solution

Answer

Coordinates of parallelogram $DEFG$ in vertex matrix is $\left[\begin{array}{cccc}2& 5& 4& 1\\ 4& 4& 1& 1\\ & & & \end{array}\right]$

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 parallelogram

Since, a parallelogram 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 parallelogram are $D\left(2,4\right),E\left(5,4\right)\text{, }F\left(4,1\right)\text{, and }G\left(1,1\right)$ 

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

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