Answer to Question #96577 in Analytic Geometry for Sami

Question #96577
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?
1
Expert's answer
2019-10-16T10:47:10-0400

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)=((kx\u2082 + x\u2081)\/(k+1), (ky\u2082 + y\u2081)\/(k+1))"

where

"A=(x\u2081, y\u2081)=(-1,-3.5)" ;

"C=(x\u2082, y\u2082)=(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)

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