Question

q r 3a + 6 v w 2a - 2 s 2a if v is the midpoint of qs and w is the midpoint of rs, then what is vs? 4 units 8 units 10 units 20 units

Explanation:

Step1: Apply Midsegment Theorem

Midsegment \( VW = \frac{1}{2}QR \), so \( 2a - 2 = \frac{1}{2}(3a + 6) \)

Step2: Solve for \( a \)

Multiply both sides by 2: \( 4a - 4 = 3a + 6 \). Subtract \( 3a \): \( a - 4 = 6 \). Add 4: \( a = 10 \)

Step3: Calculate \( VS \)

\( VS = 2a = 2(10) = 20 \)

Answer:

20 units