Question

Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y = 6.

Answer 1

Given: 

lines A 2x + 3y = 19 and B 2x + 3y + 7 = 0 also a line C 2x + 3y = 6. 

To prove: 

Line A and B are equidistant from the line C 

Proof: 

Let d₁ be the distance between lines 2x + 3y = 19 and 2x + 3y = 6, 

While d₂ is the distance between lines 2x + 3y + 7 = 0 and 2x + 3y = 6

Hence proved, the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y = 6