SOLUTION: The point (-1,-5) is equidistant from the lines 3x-4y-2=0 and 3x-4y+k=0, where k can not equal -2. Find the value of k. Please help..

Question 824807: The point (-1,-5) is equidistant from the lines 3x-4y-2=0 and 3x-4y+k=0, where k can not equal -2. Find the value of k. Please help..
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
3x-4y-2=0 same as -4y=-3x+2, y=(3/4)x-1/2.
General point is (x,(3/4)x-1/2).

3x-4y+k=0 same as -4y=-3x-k, y=(3/4)x+k/4.
General point is (x, (3/4)x+k/4).

You want each of these line to be the same distance from point (-1,-5). Using Distance Formula, these distances each are:

and
and
and

We must look very carefully at each expression and understand that must be equal to . They MUST correspond as equivalent!

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