Question

look at the diagram and evaluate. which of the statements below is false?

answer

w is the midpoint of \\(\overline{vx}\\)

wx > xy

wy < vx

wx = xy

Explanation:

Step1: Identify coordinates

From the number line: \( V = 8 \), \( W = 14 \), \( X = 20 \), \( Y = 22 \).

Step2: Check \( W \) as midpoint of \( \overline{VX} \)

Midpoint formula: \( \frac{V + X}{2} = \frac{8 + 20}{2} = 14 \), which is \( W \). So this is true.

Step3: Calculate \( WX \), \( XY \)

\( WX = |20 - 14| = 6 \); \( XY = |22 - 20| = 2 \). So \( WX > XY \) (true), \( WX = XY \) (false, since \( 6
eq 2 \)).

Step4: Check \( WY < VX \)

\( WY = |22 - 14| = 8 \); \( VX = |20 - 8| = 12 \). \( 8 < 12 \), so true.

Answer:

\( \boldsymbol{WX = XY} \) (the false statement)