Question

c is the midpoint of \\(\overline{bd}\\). if \\(bc = 2x\\) and \\(cd = x + 1\\), what is \\(cd\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint definition

Since \( C \) is the midpoint of \( \overline{BD} \), \( BC = CD \). So we set \( 2x = x + 1 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 2x - x = x + 1 - x \), which simplifies to \( x = 1 \).

Step3: Find \( CD \)

Substitute \( x = 1 \) into \( CD = x + 1 \), so \( CD = 1 + 1 = 2 \).

Answer:

2