Question

w is the midpoint of \\(\overline{vx}\\) and y is the midpoint of \\(\overline{ux}\\). if \\(uv = p + 38\\) and \\(wy = p\\), what is the value of \\(p\\)? image of a triangle-like figure with vertices v, u, x, midpoints w (of vx) and y (of ux) \\(p = \square\\)

Explanation:

Step1: Use the mid - segment theorem

Since \(W\) is the midpoint of \(\overline{VX}\) and \(Y\) is the midpoint of \(\overline{UX}\), by the mid - segment theorem in a triangle, \(WY=\frac{1}{2}UV\).

Step2: Substitute the given expressions

We know that \(UV = p + 38\) and \(WY=p\). Substituting into the equation \(WY=\frac{1}{2}UV\), we get \(p=\frac{1}{2}(p + 38)\).

Step3: Solve the equation for \(p\)

Multiply both sides of the equation \(p=\frac{1}{2}(p + 38)\) by \(2\) to get \(2p=p + 38\). Then subtract \(p\) from both sides: \(2p-p=p + 38-p\).

Answer:

\(p = 38\)