Question

The coordinates of the point is two-thirds away from (-4,3) to (5,7) is....... ?

The answer should be (2, 17/3 )
Please help me out

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

Solution is not available in text so I've posted directly from book