Question

gh bisects cf, cf = 2y - 2, and cd = 3y - 11. find cd.

Explanation:

Step1: Use the property of bisecting

Since \( \overline{GH} \) bisects \( \overline{CF} \), then \( CE = CD \). So \( 2y - 2=3y - 11 \).

Step2: Solve the equation for \( y \)

Subtract \( 2y \) from both sides: \( - 2=y - 11 \).
Add 11 to both sides: \( y = 9 \).

Step3: Find the value of \( CD \)

Substitute \( y = 9 \) into the expression for \( CD \) (\( CD=3y - 11 \)).
\( CD=3\times9 - 11=27 - 11 = 16 \).

Answer:

16