Answer to Question #96577 in Analytic Geometry for Sami

Question

line segment AC has endpoints A (-1, -3.5) and C (5,-1). Point B is on like segment AC and is located at (0.2, -3). what is the ratio of AB/BC?

Answer 1

Point B lies on the line segment AC. Let it divide the line segment in the ratio, $k:1$ , thus

$AB/BC=k$

Using the formula, coordinates of $B=(x,y)$ are given by

$(x,y)=((kx₂ + x₁)/(k+1), (ky₂ + y₁)/(k+1))$

where

$A=(x₁, y₁)=(-1,-3.5)$ ;

$C=(x₂, y₂)=(5,-1)$

Given : $B=(x,y)=(0.2,-3)$

Solving the x-coordinate for k; we get;

$0.2=(k*5 +(-1))/(k+1)$

$=(5k-1)/(k+1)$

$\implies k+1=25k-5$

$\implies 24k=6$

$\therefore k=1/4$

AB/BC=0.25 (Answer)