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) externelly 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

the ratio is 2 : 3
by applying section formula
 
 -4x2+5x3 , 7x2+3x1

    2+3             2+3

-8+15              14+4

     5                   5

7/5 ,  18/5