Question

in the diagram, line a is the perpendicular bisector of km. what is the length of km? 22 units 40 units 44 units 80 units

Explanation:

Step1: Use the property of perpendicular bisector

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

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(9x-7x - 5=7x-7x + 7\), which gives \(2x-5 = 7\).
Add \(5\) to both sides: \(2x-5 + 5=7 + 5\), so \(2x=12\).
Divide both sides by \(2\): \(x = 6\).

Step3: Find the length of \(KL\)

Substitute \(x = 6\) into \(KL=6x + 4\). Then \(KL=6\times6 + 4=36 + 4 = 22\).

Step4: Calculate the length of \(KM\)

Since \(L\) is the mid - point of \(KM\) (because \(a\) is the perpendicular bisector), \(KM = 2\times KL\).
So \(KM=2\times22 = 44\) units.

Answer:

C. 44 units