Chapter 6, Problem 28CCSR

a.

To determine

To determine if $ABCD$ is a trapezoid.

Answer to Problem 28CCSR

Yes. $ABCD$ is a trapezoid

Explanation of Solution

Given:

Vertices of a quadrilateral $ABCD$ : $A(1,1)$ , $B(1,5)$ , $C(5,5)$ , $D(7,1)$

Now, draw a quadrilateral using the given coordinates.

  

The above figure is a trapezoid because $BC$ is parallel to $AD$ which is a given condition of trapezoid.

Conclusion:

Hence, the given coordinates of the vertices are of a trapezoid.

  $ABCD$ is a trapezoid.

b.

To determine

To change the given coordinates of vertices of trapezoid into a parallelogram by moving point $B$

Answer to Problem 28CCSR

New coordinates of vertex $B$

  $(-1,5)$

Explanation of Solution

Given:

From above sub-part,

Trapezoid $ABCD$

  

To change the given trapezoid $ABCD$ into a parallelogram, move the point $B$ 2 units to the left.

So, the new coordinates of the vertex $B$ is $(-1,5)$ .

Then, coordinates of parallelogram $ABCD$ are $A(1,1)$ , $B(-1,5)$ , $C(5,5)$ , $D(7,1)$ .

  

Conclusion:

Hence, by shifting the vertex $B$ , the trapezoid $ABCD$ will change into a parallelogram.