Chapter 11.5, Problem 8IP

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 vertex $D$ .

Explanation of Solution

Given:

Coordinates of the vertices of the trapezoid $ABCD$

  $A(-3,1)$, $B(-3,4)$, $C(1,4)$, $D(-1,1)$

Graph:

By using the above coordinates, draw the graph.

  

Interpretation:

In the above graph, the shaded portion shows the trapezoid $ABCD$ .

Graph of the image:

Let $A\text{'}B\text{'}C\text{'}D$ be the image of $ABCD$ after a clockwise rotation of ${180}^0$ about the vertex $D$ .

  

Interpretation:

The shaded portion in the above graph shows the trapezoid $A\text{'}B\text{'}C\text{'}D$ .

b.

To determine

To give the coordinates of the vertices of the trapezoid $A\text{'}B\text{'}C\text{'}D\text{'}$ .

Answer to Problem 8IP

  $A\text{'}(-1,4)$ , $B\text{'}(-2,3)$ , $C\text{'}(-5,3)$ , $D\text{'}(4,-8)$

Explanation of Solution

Given:

Trapezoid $A\text{'}B\text{'}C\text{'}D\text{'}$

Calculation:

After obtaining the final image of the $ABCD,$ observe the graph to obtain the coordinates of vertices of trapezoid $A\text{'}B\text{'}C\text{'}D\text{'}.$

  

So,

Coordinates of vertices of $A\text{'}B\text{'}C\text{'}D\text{'}$

$A\text{'}(1,1)$

$B\text{'}(1,4)$

$C\text{'}(-3,4)$

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

Conclusion:

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