A-line-is-such-that-its-segment-between-the-lines-5x-y-4-0-and-3x-4y-4-0-is-bisected-at-the-point-1-5-Obtain-its-equation-

Question Number 75300 by vishalbhardwaj last updated on 09/Dec/19

A line is such that its segment between

the lines 5 x - y + 4 = 0 and 3 x + 4 y - 4 = 0

is bisected at the point (1, 5) . Obtain its

equation ?

Answered by mr W last updated on 09/Dec/19

s a y t h e e q n . i s

\frac{y - 5}{x - 1} = m

\Rightarrow y = m x + 5 - m

5 x - m x - 5 + m + 4 = 0

\Rightarrow x = \frac{1 - m}{5 - m}

3 x + 4 m x + 20 - 4 m - 4 = 0

\Rightarrow x = \frac{4 m - 16}{3 + 4 m}

\frac{1}{2} (\frac{1 - m}{5 - m} + \frac{4 m - 16}{3 + 4 m}) = 1

\Rightarrow m = \frac{107}{3}

\frac{y - 5}{x - 1} = \frac{107}{3}

\Rightarrow 107 x - 3 y - 92 = 0

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