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Question
The 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
Find the slope of the line joining the point (– 2, 6) and (4, 8)
Slope of line (m1) = `(y_2 - y_1)/(x_2 - x_1)`
= `(8- 6)/(4 + 2) = 2/6 = 1/3`
Find the slope of the line joining the points (8, 12) and (x, 24)
Slope of a line (m2) = `(24 - 12)/(x - 8) = 12/(x - 8)`
Since the two lines are perpendicular.
m1 × m2 = – 1
`1/3 xx 12/(x - 8)` = – 1
⇒ `12/(3(x - 8))` = – 1
– 1 × 3(x – 8) = 12
– 3x + 24 = 12
⇒ – 3x = 12 – 24
– 3x = – 12
⇒ x = `12/3` = 4
∴ The value of x = 4
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