Chapter 4.3, Problem 2GP

To determine

To verify the perpendicularity of given beams.

Answer to Problem 2GP

The beams are not perpendicular.

Explanation of Solution

Given:

A beam represented by $\overline{QR}$ has end points $Q\left(-6,2\right)\&R\left(-1,8\right)$ and the beam $\overline{ST}$ has end points

  $S\left(-3,6\right)\&T\left(-8,5\right)$ .

Concept used:

Two lines are perpendicular if and only if the product of their slopes is $-1$ .

Slope of a line joining the points $\left(x_1,y_1\right)\&\left(x_2,y_2\right)$ is $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Let m1 and m2 be the slopes of the beams $\overline{QR}$ and $\overline{ST}$ respectively.

Now slope of the line joining the points $Q\left(-6,2\right)\&R\left(-1,8\right)$ is,

  $m_1=\frac{8-2}{-1-\left(-6\right)}=\frac{6}{5}$

Similarly the slope of the line joining the points $S\left(-3,6\right)\&T\left(-8,5\right)$ is,

  $m_2=\frac{5-6}{-8-\left(-3\right)}=\frac{1}{5}$

Now,

  $m_1\cdot m_2=\frac{6}{5}\cdot \frac{1}{5}=\frac{6}{25}\ne -1$

Therefore, the beams are not perpendicular.