Chapter 9.2, Problem 10PSA

To determine

To find:The coordinates of Qand uses slope to show that $\Delta DEF$ is right-angle triangle.

Answer to Problem 10PSA

The coordinates of Q are $(4,-1)$

Explanation of Solution

Given information:The following information has been given

  $D=(1,3)$

  $E=(8,2)$

  $F=(7,-5)$

We know that Q is the midpoint of DF. Hence, we can say that

  $Q=\left(\frac{1+7}{2},\frac{3-5}{2}\right)=(4,-1)$

Now, for $\Delta DEF$ , we have

  $m_1{m}_2=\left(\frac{3-2}{1-8}\right)\times \left(\frac{2+5}{8-7}\right)=\frac{7}{-7}=-1$

Hence, proved that angle $\Delta DEF$ is right-angle by using the slopes.