Question

The co-ordinates of point that is 2/3 away from (-4,3) to (5,7) is

Answer 1

Let the required coordinate of the point is (x,y). Then the point cuts the line segment joining the points (-4,3) and (5,7) externally in the ratio of 2:3.
∴, x=(mx₂-nx₁)/(m-n) and y=(my₂-ny₁)/(m-n) where
(x₁,y₁)=(-4,3) and (x₂,y₂)=(5,7) and m:n=2:3
x={2.5-3.(-4)}/(2-3)=(10+12)/(-1)=-22
y=(2.7-3.3)/(2-3)=(14-9)/(-1)=-5
∴, the required coordinate is: (-22,-5)

Answer 2

let take the coordinates (a,b)
m:n=2:3
a= -4*3+5*2/(2+3)
a=-12+10/5=-2/5
b=3*3+7*2/5
b=23/5
so coordinates of the point are (-2/5,23,5)