Question

find condition that the point (x,y) lies on the line joining (3,4) and (-5,6).

Answer 1

distance between given point is √{(-5-3)+(6-4)²}
and find distances from point (x,y) from both point
then d1+d2=above distance

Answer 2

condition that the point (x,y) lies on the line joining (3,4) and (-5,6)
is the line equation joining 3 points  (3,4), (x,y) and (-5,6)
equation (y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁)
substituting....
(y-4)/(x-3) = (6-4)/(-5-3)
x+y-7 = 0