Equation of straight line midway between the lines x -2 y -1-0 and 2 x -4 y -5-0 is A- 2 x -4 y -7-0B- 2 x -4 y -3-0C- x-2 y-3-0D- 4 x -8 y -7-0

The correct option is D 4x+8y 7=0Line midway between ax+by+c_1=0 and ax+by+c_2=0 is ax+by+c_1+c_22=0 Hence, line midway between 2x+4y 2=0 and 2x+4y 5=0 is 2x+4 ...

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Standard XII

Mathematics

Condition for Two Lines to Be Parallel

Equation of s...

Question

Equation of straight line midway between the lines $x + 2 y - 1 = 0$ and $2 x + 4 y - 5 = 0$ is

2 x + 4 y - 3 = 0

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2 x + 4 y - 7 = 0

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x + 2 y - 3 = 0

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4 x + 8 y - 7 = 0

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Solution

The correct option is D $4 x + 8 y - 7 = 0$
Line midway between $a x + b y + c_{1} = 0$ and $a x + b y + c_{2} = 0$ is $a x + b y + \frac{c_{1} + c_{2}}{2} = 0$
Hence, line midway between $2 x + 4 y - 2 = 0$ and $2 x + 4 y - 5 = 0$ is $2 x + 4 y - \frac{7}{2} = 0$
$\Rightarrow 4 x + 8 y - 7 = 0$

Alternate Solution:
$2 x + 4 y - 2 = 0$ and $2 x + 4 y - 5 = 0$
Let $2 x + 4 y + k = 0$ be the required line.
Now
$\frac{| k + 2 |}{\sqrt{20}} = \frac{| k + 5 |}{\sqrt{20}} \Rightarrow | k + 2 | = | k + 5 | \Rightarrow k = - \frac{7}{2}$
So the line will be
$\Rightarrow 4 x + 8 y - 7 = 0$

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Condition for Two Lines to Be Parallel

Standard XII Mathematics

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Equation of straight line midway between the lines x+2y−1=0 and 2x+4y−5=0 is

Equation of straight line midway between the lines $x + 2 y - 1 = 0$ and $2 x + 4 y - 5 = 0$ is