SOLUTION: The magnitude of the distance from the line 5x = By + 26 to the point (3, -5) is 49/13. Determine the value of B.

Algebra ->  Coordinate-system -> SOLUTION: The magnitude of the distance from the line 5x = By + 26 to the point (3, -5) is 49/13. Determine the value of B.      Log On


   

Question 1119291: The magnitude of the distance from the line 5x = By + 26 to the point (3, -5) is 49/13. Determine the value of B.
Found 2 solutions by greenestamps, math_helper:
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


(corrected response.... the original was a half-asleep late night one.)

The distance from a point (a,b) to the line Ax+By+C=0 is given by the formula

abs%28%28Aa%2BBb%2Bc%29%2Fsqrt%28A%5E2%2BB%5E2%29%29

Convert the given equation to the required form and plug in the given numbers and we get the equation

abs%28%285%283%29%2BB%285%29-26%29%2Fsqrt%285%5E2%2BB%5E2%29%29+=+49%2F13

That's a rather ugly equation to solve with pencil and paper; a graphing calculator shows one answer is B=12 and another is an ugly probably irrational number about -1.8.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
A couple minor corrections to @greenestamps answer:
He wrote a quadratic form but it should have been ax+by+c = 0

The distance formula to (h,k) from this line is |d| = abs%28a%2Ah%2Bb%2Ak%2Bc%29%2Fsqrt%28a%5E2%2Bb%5E2%29+


Plugging in a=-5, b=B, c=26, h=3, k=-5:

+abs%28-15-5B%2B26%29%2Fsqrt%2825%2BB%5E2%29+=+49%2F13+

Which has TWO solutions for B:
1. highlight%28B=12%29+
and
2. +highlight+%28+B+=+-1649%2F912%29+