Question

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

Explanation:

Step1: Calculate \(AK\)

\(AK = 10 - 5=5\)

Step2: Check if \(K\) is mid - point of \(\overline{AB}\)

Since \(KB = 5\) and \(AK = 5\), \(AK=KB\). So \(K\) is the midpoint of \(\overline{AB}\)

Step3: Check \(B\) as mid - point of \(\overline{KT}\)

\(KB = 5\), \(BT = 4\), \(KB
eq BT\), so \(B\) is not the midpoint of \(\overline{KT}\)

Step4: Check \(AK = BT\)

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

Step5: Check \(AB = KT\)

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

Answer:

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