Chapter 4.4, Problem 2CYP

To determine

To find: Whether the beams QR and ST are perpendicular or not. Explain.

Answer to Problem 2CYP

Beams are not perpendicular to each other.

Explanation of Solution

Given information:The given beam QR has end-points $Q\left(-6,2\right),R\left(-1,8\right)$ and the beam ST has end-point $S\left(-3,6\right),T\left(-8,5\right)$ .

Concept used: If a line is perpendicular to another line then the slope of that line will be negative reciprocal.

Calculation: Slopeof the beam QR through the points $Q\left(-6,2\right),R\left(-1,8\right)$ is

  $\begin{array}{c}{m}_{QR}=\frac{8-2}{-1+6}\\ =\frac{6}{5}\mathrm{......}\left(1\right)\end{array}$

Similarly, slopeof the beam QR through the points $S\left(-3,6\right),T\left(-8,5\right)$ is,

  $\begin{array}{c}{m}_{ST}=\frac{5-6}{-8+3}\\ =\frac{1}{5}\mathrm{......}\left(2\right)\end{array}$

From (1) and (2) the slopes of beam QR and ST are not negative reciprocal to each other. Hence, the beams are not perpendicular to each other.