Question

question 2: (overline{wy}) bisects (overline{uv}) at point y. if (uy = x - 7) and (yv = 3x - 29), then determine (uv). show your algebraic thinking to earn full credit.

Explanation:

Step1: Use the definition of a bisector

Since \(\overline{WY}\) bisects \(\overline{UV}\) at \(Y\), we know that \(UY = YV\). So we set up the equation:
\(x - 7 = 3x - 29\)

Step2: Solve for \(x\)

Subtract \(x\) from both sides:
\(-7 = 2x - 29\)
Add 29 to both sides:
\(22 = 2x\)
Divide both sides by 2:
\(x = 11\)

Step3: Find the length of \(UY\) and \(YV\)

Substitute \(x = 11\) into \(UY = x - 7\):
\(UY = 11 - 7 = 4\)
Since \(UY = YV\), \(YV = 4\)

Step4: Calculate the length of \(UV\)

\(UV = UY + YV = 4 + 4 = 8\)

Answer:

\(UV = 8\)