Lydia D.
asked • 12/04/2213. In triangle ABC, centroid D is on median AM. AD = x + 6 and DM = 2x - 2. Find AM.
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1 Expert Answer
Philip P. answered • 12/04/22
Tutor
New to Wyzant
A median is the line from a vertex to the midpoint of the opposite side. The point of concurrency (intersection) of the three medians is called the centroid. The centroid divides each median into two segments in the ratio 2:1, with the larger segment nearer the vertex. So:
AD/DM = 2/1
AD = 2·DM
x = 2(2x-2)
x = 4x - 4
Solve for x. Once you have x, AM = AD + DM = x + 2x - 2.
Jose S.
Set up AD = 2 * DM 2(2x -2) = x + 6 4x - 4 = x + 6 3x = 10 x = 10/3 Plug into AM = AD + DM AM = (10/3 + 6) + [(10/3)*2]-2 AM =10/3 + 20/3 + 4 AM = 30/3 + 4 AM = 14
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12/07/22
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Mark M.
Where is M?12/04/22