The vertices of a triangle are A(- 2, 2), B(4, 6), and C(0, 10).
(a) Find, M, the point of intersection of the medians of ?ABC.
(b) Prove that the point M is two-thirds of the distance from A to the midpoint of BC.
Answers may vary.
The midpoint of AB = N = (1, 4). Then the line through C and N is y = -6x + 10
The midpoint of BC = T = (2, 8). Then the line through A and T is y= 3/2x + 5.
The point of intersection, M, of these two lines is (2/3, 6) Then AT = ?52 and AM = 2/3 ?52.
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