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Question
The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. at right angle. Find the value of h.
Solution
Let the slope of line AB passing through points A(h, 3), B(4, 1) be,
`"m"_1 = (1 - 3)/(4 - "h") = 2/("h" - 4)`
equation of second line
7x − 9y − 19 = 0
or y = `7/9"x" - 19/9`
∴ Slope of the second line, m2 = `7/9`
Since, both lines intersect each other at right angles,
∴ m1m2 = –1
= `2/("h" - 4) xx 7/9 = -1`
14 = –9(h – 4) = –9h + 36
∴ 9h = 36 – 14 = 22
h = `22/9`
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