SOLUTION: 1) find the point (x,y) on the line y=4x+5 that is equidistant from the points (-9,7) and (-8,3) 2) find the perimeter of the triangle with the vertices at (1,2), (-6,5) and (-6,-

Algebra ->  Coordinate-system -> SOLUTION: 1) find the point (x,y) on the line y=4x+5 that is equidistant from the points (-9,7) and (-8,3) 2) find the perimeter of the triangle with the vertices at (1,2), (-6,5) and (-6,-      Log On


   

Question 785377: 1) find the point (x,y) on the line y=4x+5 that is equidistant from the points (-9,7) and (-8,3)
2) find the perimeter of the triangle with the vertices at (1,2), (-6,5) and (-6,-3)
thank you!!!
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Question #1.

The line contains some general point, (x, 4x+5). The distance from this general point to one of the given points must be equal to the distance from the general point to the other given point. Setup the distance formula expressions.

From the line to (-9,7): sqrt%28%28x-%28-9%29%29%5E2%2B%284x%2B5-7%29%5E2%29
sqrt%28%28x%2B9%29%5E2%2B%284x-2%29%5E2%29
sqrt%28x%5E2%2B18x%2B81%2B16x%5E2-16x%2B4%29
sqrt%2817x%5E2%2B2x%2B85%29


From the line to (-8,3): sqrt%28%28x-%28-8%29%29%5E2%2B%284x%2B5-3%29%5E2%29
sqrt%28%28x%2B8%29%5E2%2B%284x%2B2%29%5E2%29
sqrt%28x%5E2%2B18x%2B64%2B16x%5E2%2B16x%2B4%29
sqrt%2817x%5E2%2B34x%2B68%29

These two expressions, equated and then both sides squared, give
17x%5E2%2B2x%2B85=17x%5E2%2B34x%2B68
2x%2B85=34x%2B68
85=32x%2B68
86-68=32x
32x=18
x=18%2F32=highlight%289%2F16=x%29

Use the line equation again for finding y.
y=%289%2F16%29%2A4%2B5
y=9%2F4%2B5
y=%289%2B20%29%2F4=29%2F4
highlight%28y=7%261%2F4=29%2F4%29
'
Point solution is (9/16, 29/4)