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 \(2x-5 = 7\). Then add \(5\) to both sides: \(2x-5 + 5=7 + 5\), so \(2x=12\). Divide by \(2\): \(x = 6\).

Step3: Find the length of \(KL\)

Substitute \(x = 6\) into \(KL=6x + 4\). So \(KL=6\times6 + 4=36 + 4=40\). Since \(L\) is the mid - point of \(KM\) (because line \(a\) is the perpendicular bisector), \(KM = 2KL\). But \(KL = 40\) (after substitution), so \(KM = 40\) units.

Answer:

40 units