Chapter 11.5, Problem 2GP

a.

To determine

To graph a triangle with given coordinates of the vertices and then obtaining its image after a rotation of ${270}^0$ about vertex $J$ .

Explanation of Solution

Given:

Coordinates of the vertices of $\Delta JKL$

  $J(1,4)$

  $K(1,1)$, $L(5,1)$

Graph:

By using the given coordinates, the graph is drawn below.

  

Interpretation:

In the above graph, the shaded portion shows $\Delta JKL.$

Graph of the image:

Let $\Delta J\text{'}K\text{'}L\text{'}$ be the image of $\Delta JKL$ after a clockwise rotation of ${270}^0$ about vertex $J$ .

  

Interpretation:

In the above graph, the shaded portion in the graph shows $\Delta J\text{'}K\text{'}L\text{'}.$

b.

To determine

To give the coordinates of the vertices of $\Delta J\text{'}K\text{'}L\text{'}$ .

Explanation of Solution

Given:

Coordinates of the vertices of $\Delta JKL$

  $J(1,4)$

  $K(1,1)$, $L(5,1)$

Calculation:

After obtaining the final image of the $\Delta JKL,$ observe the graph to obtain the coordinates of vertices of $\Delta J\text{'}K\text{'}L\text{'}.$

  

So,

Coordinates of vertices of $\Delta J\text{'}K\text{'}L\text{'}$

$J\text{'}(1,-4)$

$K\text{'}(4,-4)$

$L\text{'}(4,-8)$

Conclusion:

The coordinates of the vertices of $\Delta J\text{'}K\text{'}L\text{'}$ are $J\text{'}(1,-4)$ , $K\text{'}(4,-4)$ , $L\text{'}(4,-8)$ .