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Question
A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.
Solution
Co-ordinates of centroid of ΔABC are (0, 0)
∴ `0 = (x_1 + x_2 + x_3)/3`
= `(5 - 4 + y)/3`
`=> 0 = (y + 1)/3`
`=>` y + 1 = 0
∴ y = –1
Again `0 = (y_1 + y_2 + y_3)/3`
= `(x + 3 - 2)/3`
`=> 0 = (x + 1)/3`
`=>` x + 1 = 0
∴ x = –1
∴ x = –1, y = –1
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