Final answer:
GA is found by setting up the equation 2 * (CB) = GH and solving for z, then applying that value to find GA as half of GH. The final answer for GA is 17 units long.
Step-by-step explanation:
In triangle GHJ, with points G, H, and J, if A is the midpoint of GH and CB is parallel to GH and is a midsegment, by the properties of midsegments in triangles, we know that CB is half the length of GH. Additionally, given that GH = 7z - 1 and CB = 4z - 3, we can set up the equation:
2 * (4z - 3) = 7z - 1
This simplifies to:
8z - 6 = 7z - 1
Solving for z:
z = 5
Because A is the midpoint of GH, GA is half the length of GH. So, GA = (7z - 1) / 2.
Therefore, GA = (7 * 5 - 1) / 2 = (35 - 1) / 2
GA = 34 / 2
GA = 17
So, GA is 17 units long.