Question

Is the line through points P(–8, –10) and Q(–5, –12) perpendicular to the line through points R(9, –6) and S(17, –5)? Explain.

Answer 1

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Below are the choice that can be found from other source:

No; one line has zero slope, the other has no slope. 
Yes; the lines are both vertical. 
Yes; the lines have equal slopes. 
No; the lines have unequal slopes

I think the answer is the first one. 

Answer 2

Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

Step-by-step explanation:

Two lines are called perpendicular to each other if the product of their slope is -1.

Since, the slope of a line having end points $(x_1,y_1)$ and $(x_2,y_2)$ is,

$m=\frac{y_2-y_1}{x_2-x_1}$

Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),

$m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}$

While, The slope of line Joining points R(9, –6) and S(17, –5),

$m_2=\frac{-5+6}{17-9}=\frac{1}{8}$

Since,

$m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1$

Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).