Question

Given line LM and point R that lies on line LM, identify the following ratios given that point R lies a/b of the way along line LM, closer to L than M.
LR:LM
RM:LM
RL:RM

I don't understand how to do this, help.

Answer 1

Answer:

See explanation

Step-by-step explanation:

If point R lies $\frac{a}{b}$ of the way along line LM, closer to L than M, then

$LR=ax\\ \\LM=bx$

Find all needed ratios:

1. $\dfrac{LR}{LM}=\dfrac{ax}{bx}=\dfrac{a}{b}$

2. By segment addition postulate,

$LR+RM=LM\\ \\RM=bx-ax=(b-a)x,$

so

$\dfrac{RM}{LM}=\dfrac{(b-a)x}{ax}=\dfrac{b-a}{a}$

3. $RL=LR=ax\\ \\RM=(b-a)x,$

then

$\dfrac{RL}{RM}=\dfrac{ax}{(b-a)x}=\dfrac{a}{b-a}$