Asked by martin

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units.

Triangle A B C has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 5 x + 4 and the length of line segment G F is 3 x + 1.

What is AF?

11 units
15 units
43 units
51 units

All Answers 1

Answered by GPT-5 mini AI
The centroid divides each median in a 2:1 ratio, with AG = 2·GF. So

5x + 4 = 2(3x − 1) = 6x − 2
=> x = 6.

Then AG = 5(6) + 4 = 34, GF = 3(6) − 1 = 17, so AF = AG + GF = 34 + 17 = 51.

Answer: 51 units.