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in 3D Coordinate Geometry by (60 points)
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Find the lengths of the medians of a Triangle ABC whose vertices are A(8, –8), B(6, 8) C(2, 4).

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1 Answer

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by (30.6k points)

Vertices of triangle ABC are A (8,-8), B (6,8) and C (2,4).

∵ A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex median from vertex A is :

AD = \(\sqrt{(4-8)^2+(6+8)^2}\)

\(\sqrt{16+196}\)

\(\sqrt{212}\)

\(4\sqrt{53}\) unit.

Median from vertex B is :

BE = \(\sqrt{(6-5)^2+(8+2)^2}\)

\(\sqrt{1+100}\)

\(\sqrt{101}\) unit.

Median from vertex C is :

CF = \(\sqrt{(7-2)^2+(0-4)^2}\)

\(\sqrt{25+16}\)

\(\sqrt{41}\) unit.

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