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Question
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
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Solution
Let the given points be A (−2, 6), B (4, 8), P (8, 12) and Q (x, 24).
Slope of AB = m1 = \[\frac{8 - 6}{4 + 2} = \frac{2}{6} = \frac{1}{3}\]
Slope of PQ = m2 = \[\frac{24 - 12}{x - 8} = \frac{12}{x - 8}\]
It is given that the line joining A (−2, 6) and B (4, 8) and the line joining P (8, 12) and Q (x, 24) are perpendicular.
\[\therefore m_1 m_2 = - 1\]
\[ \Rightarrow \frac{1}{3} \times \frac{12}{x - 8} = - 1\]
\[ \Rightarrow x - 8 = - 4\]
\[ \Rightarrow x = 4\]
Hence, the value of x is 4.
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