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Question
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
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Solution
Let A (h,3) and B (4,1) be the given points.
The line 7x − 9y − 19 = 0 can be written as \[y = \frac{7}{9}x - \frac{19}{9}\]
So, the slope of this line is \[\frac{7}{9}\]
It is given that the line joining the points A (h,3) and B (4,1) is perpendicular to the line 7x − 9y − 19 = 0.
\[\frac{7}{9} \times \frac{1 - 3}{4 - h} = - 1\]
\[ \Rightarrow 9h - 36 = - 14\]
\[ \Rightarrow 9h = 22\]
\[ \Rightarrow h = \frac{22}{9}\]
Hence, the value of h is \[\frac{22}{9}\].
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