In triangle, G, H, I△GHI, MM is the intersection of the three medians. If G, J, equals, 32GJ=32, find J, HJH.
Given that MM is the intersection of the three medians of triangle GHI, MM divides each median into a 2:1 ratio. Therefore, MJ = 2JH.
We are also given that GJ = 32, and since GJ = GH - HJ, we have:
32 = GH - 2JH
Since MM is also a median, GH = 2MM. Therefore, we have:
32 = 2MM - 2JH
Dividing by 2:
16 = MM - JH
Since MJ = 2JH, we can substitute into the equation:
16 = MM - MJ
16 = MJ
Since MJ = 2JH, we can solve for JH:
16 = 2JH
JH = 8
Therefore, JH is equal to 8.