Question

point u is on line segment $overline{tv}$. given $tv = 3x$, $uv = x + 1$, and $tu = x$, determine the numerical length of $overline{tu}$.

Explanation:

Step1: Use segment - addition postulate

Since point U is on line segment $\overline{TV}$, we have $TV=TU + UV$. Substituting the given expressions: $3x=x+(x + 1)$.

Step2: Simplify the equation

Combine like - terms on the right - hand side: $3x=2x + 1$.

Step3: Solve for x

Subtract $2x$ from both sides of the equation: $3x-2x=2x + 1-2x$. So, $x = 1$.

Step4: Find the length of $\overline{TU}$

We know that $TU=x$. Since $x = 1$, the length of $\overline{TU}$ is 1.

Answer:

1