The equation of the straight line which passes through the intersection of the lines $x + 2 y = 5$ and $3 x + 7 y = 17$ and is perpendicular to the line $3 x + 4 y = 14$ is

4 x - 3 y + 2 = 0

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4 x + 3 y + 2 = 0

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4 x - 3 y - 2 = 0

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4 x - 3 y + 4 = 0

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Solution

The correct option is A $4 x - 3 y + 2 = 0$
Intersection of the lines $x + 2 y = 5$ and $3 x + 7 y = 17$ is $(1, 2)$
Now equation of line perpendicular to the line $3 x + 4 y = 14$ is
$4 x - 3 y = d$
$∵$ it passes through $(1, 2)$
$∴ d = - 2$
Hence equation of the line is $4 x - 3 y + 2 = 0$

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x + 2 y = 5

3 x + 7 y = 17

3 x + 4 y = 10

x - y = 1

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3 x + 4 y = 14

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