Question

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

Explanation:

Step1: Calculate the length of \(AK\)

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

Step2: Check each option

• Option 1: \(K\) is the mid - point of \(\overline{AB}\)

If \(K\) is the mid - point of \(\overline{AB}\), then \(AK = KB\). Since \(AK = 5\) and \(KB = 5\), this option is correct.

• Option 2: \(B\) is the mid - point of \(\overline{KT}\)

\(KB = 5\) and \(BT=4\), \(KB
eq BT\), so \(B\) is not the mid - point of \(\overline{KT}\).

• Option 3: \(AK = BT\)

\(AK = 5\) and \(BT = 4\), \(AK
eq BT\).

• Option 4: \(AB=KT\)

\(AB = 10\) and \(KT=KB + BT=5 + 4 = 9\), \(AB
eq KT\).

Answer:

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