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Question
Answer the following question:
Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h
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Solution
Given, A(h, 3) and B(4, 1)
∴ Slope of AB (m1) = `(1 - 3)/(4 - "h")`
∴ m1 = `2/("h" - 4)`
Slope of line 7x − 9y − 19 = 0 is m2 = `7/9`
Since line AB and line 7x − 9y − 19 = 0 are perpendicular to each other,
m1 x m2 = −1
∴ `2/("h" - 4) xx 7/9` = −1
∴ 14 = 9(4 − h)
∴ 14 = 36 − 9h
∴ 9h = 22
∴ h = `22/9`
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