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