Chapter 4.8, Problem 26PPS

To determine

The slope of each side of the triangle.

Whether the triangle is right triangle or not.

Answer to Problem 26PPS

  $\begin{array}{l}{\mathrm{m}}_{\mathrm{X}\mathrm{Y}}=\mathrm{h}\\ {\mathrm{m}}_{\mathrm{Y}\mathrm{Z}}=-\mathrm{h}\\ {\mathrm{m}}_{\mathrm{Z}\mathrm{X}}=0\end{array}$

No

Explanation of Solution

Given:

The given vertices are:

  $\begin{array}{l}\mathrm{X}\left(0,0\right)\\ \mathrm{Y}\left(1,\mathrm{h}\right)\\ \mathrm{Z}\left(2\mathrm{h},0\right)\end{array}$

Calculation:

The slope of line XY will be:

  $\begin{array}{c}{\mathrm{m}}_{\mathrm{X}\mathrm{Y}}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\\ =\frac{\mathrm{h}-0}{1-0}\\ =\mathrm{h}\end{array}$

The slope of line YZ will be:

  $\begin{array}{c}{\mathrm{m}}_{\mathrm{Y}\mathrm{Z}}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\\ =\frac{2\mathrm{h}-\mathrm{h}}{0-1}\\ =-\mathrm{h}\end{array}$

The slope of line ZX will be:

  $\begin{array}{c}{\mathrm{m}}_{\mathrm{Z}\mathrm{X}}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\\ =\frac{0-0}{2\mathrm{h}-0}\\ =0\end{array}$

As the product of no two slopes is equal to -1, there is no right angle.

Hence, the triangle formed is not a right triangle.