Question

nt Length
Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 9 x +5. Line segment K N is 14 x minus 3.

What is the length of segment LM?

units

Answer 1

Since line a is the perpendicular bisector of KM and meets KM at L, L is the midpoint so LM = KL = 9x + 5.

Set KL = KN (because both are distances from K to a point on the bisector in the given reading), so
9x + 5 = 14x − 3
5 + 3 = 14x − 9x
8 = 5x
x = 8/5

Thus LM = 9x + 5 = 9(8/5) + 5 = 72/5 + 25/5 = 97/5 units.