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Question -

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



Answer -

Given:

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

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

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

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

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