Question

if C is a point lying on the line segment AB joining A(1,1) and B(2,-3) such that 3AC = CB, then find the co-ordinates of C?

Answer 1

3AC=CB
or, AC/CB=1/3
If we denote the coordinate of C by (x,y) then
x=(mx₂+nx₁)/(m+n)
y=(my₂+ny₁)/(m+n)
Here, (x₁,y₁)=(1,1), (x₂,y₂)=(2,-3) and m:n=1:3
∴, x=(1×2+3×1)/(1+3)
=(2+3)/4
=5/4
y=(1×-3+3×1)/(1+3)
=(-3+3)/4
=0
∴, coordinate of C is (5/4,0) Ans.

Answer 2

A(1,1)__1___C____3____B(2,-3)

3AC = CB

AC / CB = 1 : 3

USING SECTION FORMULA,

C(x,y) = [(2)1 + (1)3 / 1+3 , (-3)1+(1)3/ 1+3]

C(x,y) = (2+3/4 , -3+3/4)

C(x,y) = 5/4 , 0/4

C(x,y) = 5/4 ,0