Question

look at the diagram and evaluate. which of the statements below is false?
answer
○ q is the midpoint of pr ○ qr < op
○ oq < op ○ pq = qr

Explanation:

Step1: Identify coordinates

From the number line:

• \( O \) is at \( 2 \)
• \( P \) is at \( 9 \)
• \( Q \) is at \( 12 \)
• \( R \) is at \( 15 \)

Step2: Analyze each statement

1. Q is the midpoint of PR:

Midpoint of \( PR \) is \( \frac{9 + 15}{2} = \frac{24}{2} = 12 \), which is \( Q \)'s coordinate. So this is true.

1. QR < OP:

\( QR = 15 - 12 = 3 \), \( OP = 9 - 2 = 7 \). \( 3 < 7 \), so this is true.

1. OQ < OP:

\( OQ = 12 - 2 = 10 \), \( OP = 9 - 2 = 7 \). \( 10 < 7 \) is false.

1. PQ = QR:

\( PQ = 12 - 9 = 3 \), \( QR = 15 - 12 = 3 \). So \( PQ = QR \), this is true.

Answer:

OQ < OP