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 $TV=TU + UV$. Substituting the given values, we get the equation $3x + 6=5x+2$.

Step2: Solve the equation for x

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

Step3: Find the length of $\overline{TV}$

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

Answer:

12