Question

which statement is true about the diagram?
10
5
4
a
k
b
t
k is the midpoint of \overline{ab}.
b is the midpoint of \overline{kt}.
ak = bt
ab = kt

Explanation:

Step1: Calculate the length of \(AK\)

Since \(AB = 10\) and \(KB=5\), then \(AK=AB - KB\). So \(AK = 10 - 5=5\).

Step2: Calculate the length of \(KT\)

Since \(KB = 5\) and \(BT = 4\), then \(KT=KB + BT\). So \(KT=5 + 4 = 9\).

Step3: Calculate the length of \(AB\)

\(AB = 10\)

Step4: Check each option

• For the first option: If \(K\) is the mid - point of \(\overline{AB}\), then \(AK=KB\). Since \(AK = 5\) and \(KB = 5\), this is True.
• For the second option: If \(B\) is the mid - point of \(\overline{KT}\), then \(KB=BT\). But \(KB = 5\) and \(BT=4\), so this is False.
• For the third option: \(AK = 5\) and \(BT = 4\), so \(AK

eq BT\), this is False.

• For the fourth option: \(AB = 10\) and \(KT=9\), so \(AB

eq KT\), this is False.

Answer:

\(K\) is the midpoint of \(\overline{AB}\)