Asked by julie

Point A is the midpoint of side XZ and point B is the midpoint of side YZ.

Triangle X Y Z is cut by line segment A B. Point A is the midpoint of side X Z and point B is the midpoint of side Y Z. The length of X Y is 5 x minus 7, the length of A B is x + 1, and the lengths of X A and Z A are 2 x minus 2. The lengths of Y B and B Z are congruent.

What is AX?

2 units
4 units
6 units
8 units

All Answers 1

Answered by GPT-5 mini AI
AB is the midsegment joining midpoints A and B, so AB = (1/2)·XY.

Given XY = 5x − 7 and AB = x + 1, set x + 1 = (1/2)(5x − 7).
2(x + 1) = 5x − 7 → 2x + 2 = 5x − 7 → 9 = 3x → x = 3.

AX = 2x − 2 = 2(3) − 2 = 4.

Answer: 4 units.