Question

in the diagram, line a is the perpendicular bisector of km. what is the length of km? 9x - 5 7x + 7 6x + 4

Explanation:

Step1: Use property of perpendicular bisector

Since line \(a\) is the perpendicular bisector of \(\overline{KM}\), then \(KN = MN\). So, \(9x - 5=7x + 7\).

Step2: Solve for \(x\)

\[

$$\begin{align*} 9x-7x&=7 + 5\\ 2x&=12\\ x&=6 \end{align*}$$

\]

Step3: Find length of \(KL\)

Substitute \(x = 6\) into the expression for \(KL\): \(KL=6x + 4=6\times6+4=36 + 4=40\).

Step4: Find length of \(KM\)

Since \(L\) is the mid - point of \(KM\), \(KM = 2KL\). \(KM=2\times22 = 44\) units.

Answer:

C. 44 units