Given that segment $TQ$ is $26$ units long, what is the length of $QV$ if $TQ$ and $QV$ are collinear and $TQ$ is a part of $TV$ where $TV$ is $32$ units long?

• A. $32$ units
• B. $8$ units
• C. $26$ units
• D. $31$ units

Answer: (B)

Verified step by step guidance

1. Identify the given segments and their relationships: segment \( TQ \) is 26 units long, and segment \( TV \) is 32 units long, with \( TQ \) being part of \( TV \).
2. Since \( TQ \) and \( QV \) are collinear and \( TQ \) is part of \( TV \), the length of \( TV \) is the sum of the lengths of \( TQ \) and \( QV \). This can be expressed as: \( TV = TQ + QV \).
3. Substitute the known values into the equation: \( 32 = 26 + QV \).
4. To find the length of \( QV \), isolate \( QV \) by subtracting \( 26 \) from both sides: \( QV = 32 - 26 \).
5. Simplify the expression to find the length of \( QV \).