**Finding the Centroid of a Triangle Worksheet :**

Here we are going to see some practice questions on finding centroid of the triangle.

The centroid G of the triangle with vertices A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) is

G [ (x_{1} + x_{2} + x_{3})/3, (y_{1} + y_{2} + y_{3})/3 ]

(1) Find the centroid of the triangle whose vertices are

(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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