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Question

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

A
2x+4y3=0
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B
2x+4y7=0
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C
x+2y3=0
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D
4x+8y7=0
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Solution

The correct option is D 4x+8y7=0
Line midway between ax+by+c1=0 and ax+by+c2=0 is ax+by+c1+c22=0
Hence, line midway between 2x+4y2=0 and 2x+4y5=0 is 2x+4y72=0
4x+8y7=0

Alternate Solution:
2x+4y2=0 and 2x+4y5=0
Let 2x+4y+k=0 be the required line.
Now
|k+2|20=|k+5|20|k+2|=|k+5|k=72
So the line will be
4x+8y7=0

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