Q1 of 77 Page 7


Find the centroid of the triangle whose vertices are : (3, -5), (-7, 4), (10,-2).


∵ The centroid of the triangle ABC with A(x 1, y 1, ), B(x 2, y 2 ) and C(x 3, y 3, ) is ∴ The centroid of the triangle whose vertices are A(3, -5), B(-7, 4), C(10, -2)

So, the centroid = (2, -1)

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2
Find the centroid of the triangle whose vertices are : (2, 1), (5, 2), (3,4).
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Find the third vertex of a triangle, if two of its vertices are at (-3, 1)and (0, -2) and the centroid is at the origin.
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Prove that the diagonals of a rectangle bisect each other and are equal. (Hint:With O as origin, let the vertices of the rectangle be (0, 0), (a, 0), (a, b)and (0, b)).
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Show that the points A(1, 0), B(5, 3), C(2, 7) and D(-2, 4) are thevertices of a parallelogram. (Hint: Diagonals of a parallelogram bisecteach other).