Question

question
look at the diagram and evaluate. which of the statements below is false?
diagram: number line from 0 to 24, with points m (12), n (15), o (18), p (23)
answer
○ mp > op ○ n is the midpoint of $overline{mo}$
○ op < no ○ np > op

Explanation:

To solve this, we first find the positions of each point:

• \( M = 12 \), \( N = 15 \), \( O = 18 \), \( P = 23 \)

Analyze each option:

1. \( \boldsymbol{MP > OP} \)

• \( MP = P - M = 23 - 12 = 11 \)
• \( OP = P - O = 23 - 18 = 5 \)
• \( 11 > 5 \), so \( MP > OP \) is true.

2. \( \boldsymbol{N} \) is the midpoint of \( \boldsymbol{\overline{MO}} \)

• Midpoint of \( MO \): \( \frac{M + O}{2} = \frac{12 + 18}{2} = 15 \), which is \( N \). So this is true.

3. \( \boldsymbol{OP < NO} \)

• \( OP = 5 \) (from above)
• \( NO = O - N = 18 - 15 = 3 \)
• \( 5 < 3 \) is false (since \( 5 > 3 \)).

4. \( \boldsymbol{NP > OP} \)

• \( NP = P - N = 23 - 15 = 8 \)
• \( OP = 5 \)
• \( 8 > 5 \), so \( NP > OP \) is true.

Answer:

\( \boldsymbol{OP < NO} \) (the false statement)