Answer :

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


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