Question

CONNECTING CONCEPTS In GHJ, A is the midpoint of GH, CB is a midsegment, and CB|| GH. What is GA, when

GH=7z-1 and CB = 4z - 3 ?
GA=

Answer 1

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.