find the point (x,y) on the line y=4x+5 that is equidistant from the points (-9,7) and (-8,3)

Question

find the point (x,y) on the line y=4x+5 that is equidistant from the points (-9,7) and (-8,3)

Answer 1

(-9 - x)² + (7 - y)² = (-8 - x)² + ( 3 - y)² ----> x = 4y - 57/2  (eq. 1)

 

y = 4x + 5  (eq. 2)

 

substitute eq. 2 to eq. 1

 

x = 4(4x + 5) - 57/2

 

solve above equation.

 

x = 17/30

 

y = 109/15