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in 3D Coordinate Geometry by (50.2k points)
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The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4). Find its vertices. Also find the centriod of the triangle.

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Given; The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4).

Let he vertices be A(x1, y1, z1), B(x2, y2, z2) and A(x3, y3, z3) respectively.

∴ x2 = −1,

y2 = 6,

z2 = −7.

∴ x1 = 2 − x2 = 3,

y1 = 10 − y2 = 4,

z1 = −4 – z2 = 5.

∴ x3 = – x2 = 1,

y3 = 8 – y2 = 2,

z3 = −4 − z2 = 3.

∴ A(−1, 6, −7), B(3, 4, 5), C(1, 2, 3) are the required vertices.

Centroid of a triangle is given by the average of the coordinates of its vertices or midpoint of sides.

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