Question

point u is on line segment $overline{tv}$. given $uv = 2, tu = 5x$, and $tv = 3x + 6$, determine the numerical length of $overline{tv}$.

Explanation:

Step1: Use segment - addition postulate

Since point U is on line segment $\overline{TV}$, we have $TV=TU + UV$.
Substitute the given expressions: $3x + 6=5x+2$.

Step2: Solve the equation for x

Subtract $3x$ from both sides: $6 = 2x+2$.
Subtract 2 from both sides: $4 = 2x$.
Divide both sides by 2: $x = 2$.

Step3: Find the length of TV

Substitute $x = 2$ into the expression for $TV$: $TV=3x + 6$.
$TV=3\times2+6$.
$TV=6 + 6=12$.

Answer:

12