If A (x,y) is a point on the joining the points which are equidistant from B(2,-3)and C (-4,5) then prove that 4x+3y+1=0

Question

Give solution stepwise 

USE concept of coordinate geometry of grade 9.

Answer 1

Since the point is colinear, the midpoint is: [(2+ -4)/2, (-3+5)/2]=(-1,1)

 

Please note:   You do not need to find the midpoint to solve the equation.

 

Pick one point (-4,5)....................>4(-4) + 3(5) +1=0
Pick the other point (2,-3).................> 4(2) +3(-3) + 1=0

 

If both points listed solve the equation, then the equation is a true solution to those points.

 

The midpoint solution is just a bonus.  :)