Question

1. if km is the perpendicular bisector of jl, find x.

4x + 9
11x - 61

Explanation:

Step1: Apply the perpendicular bisector theorem

According to the perpendicular bisector theorem, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. So, \(4x + 9=11x-61\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides:
\(4x + 9-4x=11x-61 - 4x\)
\(9 = 7x-61\)
Add \(61\) to both sides:
\(9+61=7x-61 + 61\)
\(70=7x\)
Divide both sides by \(7\):
\(x=\frac{70}{7}\)

Answer:

\(x = 10\)