Chapter 4, Problem 9CR

To determine

A figure is given as follows:

And we have to choose the correct option from four given alternatives.

Answer to Problem 9CR

The correct option is “B”.

Explanation of Solution

By looking carefully we can find that dotted line passes through points

(-2, 10) and (2,-2)

So its slope, is $m_1=\frac{-2-10}{2-(-2)}=\frac{-12}{4}=-3$

By looking carefully again we can find that darked line passes through points

(10, 8) and (-2, 4)

So its slope, is $m_2=\frac{4-8}{-2-10}=\frac{-4}{-12}=\frac{1}{3}$

Now since, $m_1\times m_2=-3\times \frac{1}{3}=-1$

  $\Rightarrow$$m_1{\text{ and m}}_2$ are negative reciprocals

  $\Rightarrow$ The two lines are perpendicular because there slopes are negative reciprocals.