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Question
The co-ordinates of the centroid of a triangle PQR are (2, –5). If Q = (–6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.
Solution
Let co-ordinates of P be (x, y)
And of centroid G are (2, –5)
∴ `2 = (x_1 + x_2 + x_3)/3`
= `(x - 6 + 11)/3`
= `(x + 5)/3`
`=>` x + 5 = 6
∴ x = 6 – 5 = 1
And `-5 = (y_1 + y_2 + y_3)/3`
= `(y + 5 + 8)/3`
= `(y + 13)/3`
`=>` y + 13 = –15
∴ y = –15 – 13
= –28
Hence, co-ordinates of vertex P are (1, –28)
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Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
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