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.
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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: 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,
\(m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12} eq -1\)
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).