Question

look at the diagram and evaluate. which of the statements below is true?
number line with h at 3, i at 11, j at 15, k at 19 (marked on the line: 0 to 24 with arrows)
answer
○ hk > ik ○ i is the midpoint of \\(\overline{hj}\\)
○ hi < jk ○ ik < jk

Explanation:

To solve this, we first find the positions of points \( H = 3 \), \( I = 11 \), \( J = 15 \), \( K = 19 \). Then we calculate the lengths of the segments:

Step 1: Calculate \( HK \), \( IK \), \( HI \), \( JK \)

• \( HK = K - H = 19 - 3 = 16 \)
• \( IK = K - I = 19 - 11 = 8 \)
• \( HI = I - H = 11 - 3 = 8 \)
• \( JK = K - J = 19 - 15 = 4 \)

Step 2: Evaluate each option

• Option 1: \( HK > IK \)

\( HK = 16 \), \( IK = 8 \). Since \( 16 > 8 \), this is true. But let's check others to be sure.

• Option 2: \( I \) is the midpoint of \( \overline{HJ} \)

Midpoint of \( HJ \) should be \( \frac{H + J}{2} = \frac{3 + 15}{2} = 9 \), but \( I = 11
eq 9 \). False.

• Option 3: \( HI < JK \)

\( HI = 8 \), \( JK = 4 \). \( 8 < 4 \) is false.

• Option 4: \( IK < JK \)

\( IK = 8 \), \( JK = 4 \). \( 8 < 4 \) is false.

Answer:

\( \boldsymbol{HK > IK} \) (the first option)