SOLUTION: the angle from the line through (x,-1) and (-3,-5) to the line through (2,-5) and (4,1) is 45. find x

Algebra ->  Angles -> SOLUTION: the angle from the line through (x,-1) and (-3,-5) to the line through (2,-5) and (4,1) is 45. find x      Log On


   

Question 1033779: the angle from the line through (x,-1) and (-3,-5) to the line through (2,-5) and (4,1) is 45. find x
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The line through the points (4,1) and (2,-5) has a slope m%5B2%5D+=+%281--5%29%2F%284-2%29+=+3, while the line through the points (-3,-5) and (x,-1) has slope m%5B1%5D+=+%28-1--5%29%2F%28x--3%29+=+4%2F%28x%2B3%29.
Let theta be the positive, acute angle between the two lines.
==>
==> tan+45%5Eo+=+1+=+%283x%2B5%29%2F%28x%2B15%29, after simplification.
==> x+15 = 3x+5 ==> 10 = 2x ==> highlight%28x+=+5%29.