Question

v is the midpoint of wz and x is the midpoint of wy. if yz = p and vx = p - 44, what is the value of p?

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
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

Given \(YZ = p\) and \(VX=p - 44\). Substituting into the equation \(VX=\frac{1}{2}YZ\), we get \(p-44=\frac{1}{2}p\).

Step3: Solve the equation for \(p\)

Subtract \(\frac{1}{2}p\) from both sides: \(p-\frac{1}{2}p-44=\frac{1}{2}p-\frac{1}{2}p\), which simplifies to \(\frac{1}{2}p-44 = 0\).
Then add \(44\) to both sides: \(\frac{1}{2}p-44 + 44=44\), so \(\frac{1}{2}p=44\).
Multiply both sides by \(2\): \(p = 88\).

Answer:

\(88\)