Question

A perpendicular bisector intersects line segment A C at point B. The bisector also contains points E and D. Line segment A B is 3 x minus 2. Line sector A D is 8 x minus 1. Line sector D C is 6 x + 9.
What is the measure of AC?

5 units
13 units
26 units
39 units

Answer 1

Because D is on the perpendicular bisector of AC, it is equidistant from A and C, so AD = DC:

8x − 1 = 6x + 9 → 2x = 10 → x = 5.

Then AB = 3x − 2 = 15 − 2 = 13. Since B is the midpoint, AC = 2·AB = 26.

Answer: 26 units.