Question

look at the diagram and evaluate. which of the statements below is true?
number line with u at 5, v at 7, w at 12, x at 17 (0 to 24 marked)
answer
○ ux < uv ○ v is the midpoint of \\(\overline{uw}\\)
○ wx > uv ○ vx < vw

Explanation:

Step1: Find coordinates of points

U: 5, V: 7, W: 12, X: 17.

Step2: Calculate segment lengths

• \( UV = 7 - 5 = 2 \)
• \( UW = 12 - 5 = 7 \), midpoint of \( UW \) would be at \( 5 + \frac{7}{2} = 8.5 \), not V (7). So "V is midpoint of \( \overline{UW} \)" is false.
• \( WX = 17 - 12 = 5 \), \( 5 > 2 \), so \( WX > UV \) is true.
• \( VX = 17 - 7 = 10 \), \( VW = 12 - 7 = 5 \), \( 10 < 5 \) is false.
• \( UX = 17 - 5 = 12 \), \( 12 < 2 \) is false.

Answer:

WX > UV (the option "WX > UV")