Question

start up
find the length of lo if m is between l and o.
lm = 7x - 9
mo = 14 inches and lo = 10x - 7
lesson 3: locating points using ratios
benchmarks: ma.912.gr.3.3 use coordinate geometry to solve mathematical and real - world geometric problems involving lines, circles, triangles and quadrilaterals.
learning objectives:
□ use coordinate geometry to solve mathematical geometric problems involving lines.
□ use coordinate geometry to solve real - world geometric problems involving lines.

Explanation:

Step1: Apply segment - addition postulate

Since M is between L and O, then $LO=LM + MO$.
Substitute $LM = 7x - 9$, $MO=14$ inches, and $LO = 10x-7$ into the equation:
$10x-7=(7x - 9)+14$.

Step2: Simplify the right - hand side of the equation

$(7x - 9)+14=7x+(-9 + 14)=7x + 5$.
So the equation becomes $10x-7=7x + 5$.

Step3: Solve for x

Subtract $7x$ from both sides:
$10x-7x-7=7x-7x + 5$,
$3x-7=5$.
Add 7 to both sides:
$3x-7 + 7=5 + 7$,
$3x=12$.
Divide both sides by 3:
$x = 4$.

Step4: Find the length of LO

Substitute $x = 4$ into the expression for $LO$:
$LO=10x-7$.
$LO=10\times4-7$.
$LO=40 - 7$.
$LO = 33$ inches.

Answer:

33 inches