Chapter 13.3, Problem 15WE

To determine

To find the type of quadrilateral HIJK is.

Answer to Problem 15WE

The points HIJK are Trapezoid.

Explanation of Solution

Given information: The points are,

  $H\left(0,0\right)I\left(5,0\right)J\left(7,9\right)K\left(1,9\right)$ .

Calculation: The required solutions is obtained as,

  $\begin{array}{l}H\left(0,0\right)\text{, }I\left(5,0\right)\text{, }J\left(7,9\right)\text{, }K\left(1,9\right)\\ HI=\sqrt{5^2+0^2}=5\\ IJ=\sqrt{2^2+9^2}=\sqrt{85}\\ JK=\sqrt{6^2+0^2}=6\\ KH=\sqrt{1^2+9^2}=\sqrt{82}\end{array}$

Now, find the slopes,

  $\begin{array}{l}{m}_{HI}=\frac{0-0}{5-0}=0\\ m_{IJ}=\frac{9-0}{7-5}=\frac{9}{2}\\ m_{JK}=\frac{9-9}{1-7}=0\\ m_{KH}=\frac{9-0}{5-0}=\frac{9}{5}\end{array}$

So, $m_{HI}=m_{JK}$

Hence, it is Trapezoid.