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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.
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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