Question

u is the midpoint of $overline{tv}$. if $uv = 3x$ and $tv = 4x + 4$, what is $uv?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(U\) is the mid - point of \(\overline{TV}\), then \(UV=\frac{1}{2}TV\). Given \(UV = 3x\) and \(TV=4x + 4\), we have \(3x=\frac{1}{2}(4x + 4)\).

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(3x=\frac{1}{2}(4x + 4)\) by 2 to get \(6x=4x + 4\). Subtract \(4x\) from both sides: \(6x-4x=4x + 4-4x\), which simplifies to \(2x=4\). Divide both sides by 2: \(x = 2\).

Step3: Find the value of \(UV\)

Substitute \(x = 2\) into the expression for \(UV\). Since \(UV = 3x\), then \(UV=3\times2=6\).

Answer:

6