Question

in the diagram, line a is the perpendicular bisector of \\( \overline { k m } \\). what is the length of \\( \overline { k m } \\)? 22 units 40 units 44 units 80 units

Explanation:

Step1: Set up the equation for \(NK = NM\)

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

Step2: Solve 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 by \(2\): \(x=\frac{12}{2}=6\).

Step3: Find the length of \(KL\)

Substitute \(x = 6\) into \(KL=6x + 4\). Then \(KL=6\times6+4=36 + 4=40\).

Step4: Calculate the length of \(KM\)

Since \(L\) is the mid - point of \(KM\) (because line \(a\) is the perpendicular bisector), \(KM = 2\times KL\).
So \(KM=2\times40 = 80\).

Answer:

80 units