Question

look at the diagram and evaluate. which of the statements below is true?
number line with v at 8, w at 11, x at 14, y at 18 (marked on a line from 0 to 24)
answer
○ wx = xy ○ vy > wx
○ x is the midpoint of \\(\overline{wy}\\) ○ wx > xy

Explanation:

Step1: Find coordinates of points

V: 8, W: 11, X: 14, Y: 18.

Step2: Calculate segment lengths

WX: \( 14 - 11 = 3 \)
XY: \( 18 - 14 = 4 \)
VY: \( 18 - 8 = 10 \)
WY: \( 18 - 11 = 7 \), midpoint of WY: \( 11 + \frac{7}{2} = 14.5
eq 14 \) (X is at 14).

Step3: Evaluate statements

• \( WX = XY \): \( 3

eq 4 \) (False)

• \( VY > WX \): \( 10 > 3 \) (True)
• X is midpoint of \( \overline{WY} \): False (as above)
• \( WX > XY \): \( 3 > 4 \) (False)

Answer:

VY > WX