Question

The coordinates of the point that is two third 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

Answer:

Step-by-step explanation:

Given points: A(-4,3) and B(5,7)

Let’s assume the point as P(x,y) which is two thirds away A and B

2/3:1/3 = 2:1

So the ratio is 2:1 i.e., m=2 and n=1

Formula used:

Section formula i.e., (mx2+mx1/m+n , my2 +my1/m+n)

=> [2(5)+1(-4)/2+1] , [2(7) - 1(3)/2+1]

=> [10-4/3 , 14+3/3]

=> (2,17/3)

Hence, the answer is P(x,y) is P(2,17/3)