Question

prove that the line 5x-2y-1=0is mid parallel to the line 5x-2y-9=0 and 5x-2y+7=0

Answer 1

this is your answer of this question

Answer 2

Given:

Line to be proved parallel: 5x - 2y - 1 = 0

Line 1: 5x - 2y - 9 = 0

Line 2: 5x - 2y + 7 = 0

To prove:

Same distance between the line and the other two parallel lines.

Proof:

To find the distance between two parallel lines,

c1 - c2 /√a^2 + b^2

So,

Distance between 5x - 2y - 1 = 0 and 5x - 2y - 9 = 0 is 8 / √29

Distance between 5x - 2y - 1 = 0 and 5x - 2y + 7 = 0 is 8 / √29

It is proven that the line 5x - 2y - 1 = 0 is mid-parallel to the lines 5x - 2y - 9 = 0 and 5x - 2y + 7 = 0 as their respective distance is 8 / √29

Hence, Proved.

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