Question

v is the midpoint of \\( \overline { wz } \\) and x is the midpoint of \\( \overline { wy } \\).
if yz = s and vx = s - 38, what is the value of s?

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. Here, since \(V\) is the midpoint of \(WZ\) and \(X\) is the midpoint of \(WY\), then \(VX=\frac{1}{2}YZ\).

Step2: Substitute the given values

We know that \(YZ = s\) and \(VX=s - 38\). Substituting into the equation \(VX=\frac{1}{2}YZ\), we get \(s-38=\frac{1}{2}s\).

Step3: Solve the equation for \(s\)

Subtract \(\frac{1}{2}s\) from both sides: \(s-\frac{1}{2}s-38 = 0\), which simplifies to \(\frac{1}{2}s-38=0\). Then add 38 to both sides: \(\frac{1}{2}s=38\). Multiply both sides by 2: \(s = 76\).

Answer:

\(76\)