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Question
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Options
(12, 9)
(9, 12)
(4, 3)
(3, 4)
Solution
(4, 3)
Let P(x1, y1), Q(x2, y2), R(x3, y3) be the co-ordinates of the vertices of a triangle.
Given that x1 + x2 + x3 = 12 and y1 + y2 + y3 = 9
∴ Co-ordinates of the centroid S(x, y) are
`x = (x_1 + x_2 + x_3)/3 "and" y = (y_1 + y_2 + y_3)/3`
`x = (12)/3 "and" y = (9)/3`
`x = 4 "and" y = 3`
∴ S(x, y) = (4, 3).
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