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A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. Let's try this out with a particular triangle. Consider the triangle \(ABC \) with \(A = (5,4), B = (-9, 6), C = (1, -4)\).

(a) Let  \(D, E, F\) be the midpoints of  \(\overline{BC},\overline{AC},\overline{AB}\)  respectively. Find the equations of medians   and \(\overline{AD}, \overline{BE},\overline{CF}.\)

(b) Show that the three medians in part (a) all pass through the same point.

 Mar 21, 2024

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