Chapter 7.4, Problem 62SPR

To determine

To verify whether the given quadrilateral is trapezoid or isosceles trapezoid.

Answer to Problem 62SPR

Trapezoid.

Explanation of Solution

Given:

Thevertices of quadrilateral are $A(-3,3),B(-4,-1),C(5,-1)$ and $D(2,3)$

Calculation:

Let us find all the slopes

Slope $AB=\frac{-1-3}{-4+3}=\frac{-4}{-1}=4$

Slope $CD=\frac{3+1}{2-5}=\frac{4}{-3}=-\frac{4}{3}$

Slope $BC=\frac{-1+1}{5+4}=\frac{0}{9}=0$

Slope $AD=\frac{3-3}{2+3}=0$

  $\begin{array}{l}AB=\sqrt{{(-4+3)}^2+{(-1-3)}^2}=\sqrt{17}\\ CD=\sqrt{{(2-5)}^2+{(3+1)}^2}=5\end{array}$

Since the legs are not equal it is a trapezoid.