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The co-ordinates of the centroid of a triangle ABC are (1, -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3, -4) and (0, 5) respectively?

The co-ordinates of the centroid of a triangle ABC are (1, -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3, -4) and (0, 5) respectively? Correct Answer (0, -13)

Let the co-ordinates of the vertex C be (x, y).

Then,

Centroid = (3 + 0 + x/3, -4 + 5 + y/3) = (1, -4)

⇒ 3 + x/3 = 1                       and ⇒ 1 + y/3 = -4

⇒ 3 + x = 3                          ⇒ 1 + y = -12

⇒ x = 0                                ⇒ y = -13

∴ Co-ordinates of the vertex C are (0, -13).

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