(1) Find the centroid of the triangle.
(i) (2, −4), (−3, −7) and (7, 2)
(ii) (−5,−5), (1,−4) and (−4,−2) Solution
(2) If the centroid of a triangle is at (4,−2) and two of its vertices are (3,−2) and (5,2) then find the third vertex of the triangle Solution
(3) Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).
(4) Th e vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of √(h + k)2 + (h + 3k)2. Solution
(5) Orthocentre and centroid of a triangle are A(−3, 5) and B(3, 3) respectively. If C is the circumcentre and AC is the diameter of this circle, then find the radius of the circle. Solution
(6) ABC is a triangle whose vertices are A(3, 4), B(−2, −1) and C(5, 3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D. Solution
(7) If (3/2, 5) (7, -9/2) and (13/2, -13/2) are mid-points of the sides of a triangle, then find the centroid of the triangle. Solution
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