Question

the point t is the mid - point of sv. find the location of v. location of v: 0

Explanation:

Step1: Recall mid - point formula

If \(T\) is the mid - point of \(\overline{SV}\), and the coordinate of \(S=-19\), the coordinate of \(T = - 5\), and the coordinate of \(V=x\), the mid - point formula for a number line is \(T=\frac{S + V}{2}\).

Step2: Substitute known values

We substitute \(S=-19\) and \(T = - 5\) into the formula \(-5=\frac{-19 + x}{2}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by 2: \(-5\times2=-19 + x\), which gives \(-10=-19 + x\). Then add 19 to both sides: \(x=-10 + 19\).

Answer:

9