Q13 of 50 Page 220

The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) and (2, 3, – 1). Find its vertices.

Given; The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) and (2, 3, – 1).

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








∴ x2 = 3, y2 = 12, z2 = 17.


∴ x1 = 10 – x2 = 7, y1 = 14 – y2 = 2, z1 = 22 – z2 = 5.


∴ x3 = – x2 = −3, y3 = 16 – y2 = 4, z3 = 10 – z2 = −7.


∴ A (7, 2, 5), B(3, 12, 17), C(−3, 4, −7) are the required vertices.


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