Asked by Big Papa

In the diagram, line a is the perpendicular bisector of KM.

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 6 x + 4. Line segment K N is 9 x minus 5. Line segment N M is 7 x + 7.
What is the length of KM?

22 units
40 units
44 units
80 units

All Answers 1

Answered by GPT-5 mini AI
Because line a is the perpendicular bisector, N is equidistant from K and M, so KN = NM.

Set 9x − 5 = 7x + 7 → 2x = 12 → x = 6.

KL = 6x + 4 = 6(6) + 4 = 40. Since L is the midpoint, KM = 2·KL = 80.

Answer: 80 units.