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..

Algebra ->  Points-lines-and-rays -> 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..      Log On


   

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) About Me  (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:

sqrt%28%28x%2B1%29%5E2%2B%28%283%2F4%29x-1%2F2%2B5%29%5E2%29 and sqrt%28%28x%2B1%29%5E2%2B%28%283%2F4%29x%2Bk%2F4%2B5%29%5E2%29
sqrt%28%28x%2B1%29%5E2%2B%28%283%2F4%29x%2B11%2F2%29%5E2%29 and sqrt%28%28x%2B1%29%5E2%2B%28%283%2F4%29x%2B%28k%2B20%29%2F4%29%5E2%29
sqrt%28%28x%2B1%29%5E2%2B%28%283x%2B22%29%2F4%29%5E2%29 and sqrt%28%28x%2B1%29%5E2%2B%28%283x%2Bk%2B20%29%2F4%29%5E2%29

We must look very carefully at each expression and understand that %283x%2B22%29%2F4 must be equal to %283x%2Bk%2B20%29%2F4. They MUST correspond as equivalent!

%283x%2B22%29=%283x%2Bk%2B20%29
highlight%28highlight%28k=2%29%29