Chapter 11.5, Problem 3GP

a.

To determine

To graph a figure with given coordinates of the vertices and then obtaining its image after a rotation of ${180}^0$ about the origin.

Explanation of Solution

Given:

Coordinates of the vertices of the figure $DFGH$

  $D(1,1)$ , $F(2,3)$, $G(5,3)$, $H(5,1)$

Graph:

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

  

Interpretation:

In the above graph, the shaded portion shows figure $DFGH$ .

Graph of the image:

Let $D\text{'}F\text{'}G\text{'}H\text{'}$ be the image of $DFGH$ after a clockwise rotation of ${180}^0$ about the origin.

  

Interpretation:

The shaded portion in the above graph shows the figure $D\text{'}F\text{'}G\text{'}H\text{'}$ .

b.

To determine

To give the coordinates of the vertices of the figure $D\text{'}F\text{'}G\text{'}H\text{'}$ .

Answer to Problem 3GP

  $D\text{'}(-1,4)$ , $F\text{'}(-2,3)$ , $G\text{'}(-5,3)$ , $H\text{'}(4,-8)$

Explanation of Solution

Given:

Coordinates of the vertices of the figure $DFGH$

  $D(1,1)$ , $F(2,3)$, $G(5,3)$, $H(5,1)$

Calculation:

After obtaining the final image of the $DFGH,$ observe the graph to obtain the coordinates of vertices of $D\text{'}F\text{'}G\text{'}H\text{'}.$

  

So,

Coordinates of vertices of $D\text{'}F\text{'}G\text{'}H\text{'}$

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

$F\text{'}(-2,3)$

$G\text{'}(-5,3)$

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

Conclusion:

Therefore, the coordinates of the vertices of figure $D\text{'}F\text{'}G\text{'}H\text{'}$ are $D\text{'}(-1,4)$ , $F\text{'}(-2,3)$ , $G\text{'}(-5,3)$ , $H\text{'}(4,-8).$