Question

which statement is true about the diagram?
diagram: points a, k, b, t on a line segment. a to b is labeled 10, k to b is labeled 5, b to t is labeled 4.
options:

• b is the midpoint of $overline{kt}$
• k is the midpoint of $overline{ab}$
• $ab = kt$
• $ak = bt$

Explanation:

Step1: Calculate AK

Given \( AB = 10 \) and \( KB = 5 \), so \( AK = AB - KB = 10 - 5 = 5 \).

Step2: Compare AK and BT

Given \( BT = 4 \)? Wait, no, wait. Wait, the diagram: \( AB = 10 \), \( KB = 5 \), so \( AK = 10 - 5 = 5 \). \( BT = 4 \)? Wait, no, maybe I misread. Wait, the points: A---K---B---T. \( AB = 10 \), \( KB = 5 \), so \( AK = 5 \). \( BT = 4 \)? Wait, no, maybe the length from B to T is 4? Wait, no, let's re - check. Wait, the problem: Let's see the options. The last option is \( AK = BT \)? Wait, no, \( AK = 5 \), \( BT = 4 \)? Wait, no, maybe I made a mistake. Wait, no, the second option: K is the midpoint of AB. Because \( AB = 10 \), \( AK = 5 \), \( KB = 5 \), so K is the midpoint of AB. Let's verify each option:

1. B is the midpoint of KT: \( KT = KB + BT = 5 + 4 = 9 \), \( KB = 5 \), \( BT = 4 \), not equal, so B is not the midpoint.
2. K is the midpoint of AB: \( AB = 10 \), \( AK = 10 - 5 = 5 \), \( KB = 5 \), so \( AK = KB \), so K is the midpoint.
3. \( AB = KT \): \( AB = 10 \), \( KT = 5 + 4 = 9 \), not equal.
4. \( AK = BT \): \( AK = 5 \), \( BT = 4 \), not equal.

So the correct statement is "K is the midpoint of \(\overline{AB}\)".

Answer:

K is the midpoint of \(\overline{AB}\) (the second option among the given options: "K is the midpoint of \(\overline{AB}\)")