Question

question
look at the diagram and evaluate. which of the statements below is true?
diagram: number line from 0 to 24, points u at 1, v at 10, w at 13, x at 16
answer
○ uv = vw
○ ux < wx
○ w is the midpoint of \\(\overline{vx}\\)
○ uv < wx

Explanation:

Step1: Find coordinates of points

U is at 1, V at 10, W at 13, X at 16.

Step2: Calculate segment lengths

• \( UV = 10 - 1 = 9 \)
• \( VW = 13 - 10 = 3 \)
• \( WX = 16 - 13 = 3 \)
• \( UX = 16 - 1 = 15 \)

Step3: Evaluate each option

• \( UV = VW \): \( 9

eq 3 \), false.

• \( UX < WX \): \( 15 < 3 \), false.
• \( W \) midpoint of \( \overline{VX} \): Midpoint of V(10) and X(16) is \( \frac{10 + 16}{2} = 13 \), which is W. True? Wait, but check \( UV < WX \): \( 9 < 3 \)? No, wait, earlier miscalculation. Wait, \( UV = 10 - 1 = 9 \), \( WX = 16 - 13 = 3 \). Wait, no, wait the coordinates: U is at 1, V at 10: distance 9. V at 10, W at 13: distance 3. W at 13, X at 16: distance 3. So \( UV = 9 \), \( WX = 3 \), so \( UV > WX \)? Wait, no, the option "W is the midpoint of \( \overline{VX} \)": V is 10, X is 16. Midpoint is (10+16)/2 = 13, which is W. So that's true? Wait but let's recheck the options. Wait the options are:

1. \( UV = VW \): 9 vs 3: false.

1. \( UX < WX \): 15 vs 3: false.

1. \( W \) is the midpoint of \( \overline{VX} \): V(10), X(16). Midpoint is 13, which is W. So true?

1. \( UV < WX \): 9 < 3: false.

Wait, but wait, maybe I misread the coordinates. Let me check again. The number line: U is at 1, V at 10, W at 13, X at 16. So VX is from 10 to 16, length 6. Midpoint is at 10 + 3 = 13, which is W. So W is the midpoint of VX. So that statement is true. Wait but let's check the other option "UV < WX": UV is 9, WX is 3, so 9 < 3 is false. So the correct statement is "W is the midpoint of \( \overline{VX} \)". Wait but let's confirm:

Midpoint formula: for points V (x₁ = 10) and X (x₂ = 16), midpoint is \( \frac{x₁ + x₂}{2} = \frac{10 + 16}{2} = 13 \), which is the coordinate of W. So yes, W is the midpoint of VX.

Answer:

W is the midpoint of \(\overline{VX}\)