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High School Mathematics - 2
9.16 Centroid of a Triangle

To find the centroid of a triangle whose vertices are given

Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle ABC. Let AD be the median bisecting the base.
Then D = {(x2 + x3)/2, (y2 + y3)/2}
Now the point G on AD, which divides it internally in the ratio 2:1, is the centroid. If (x,y) are the coordinates of G, then
x = 2x(x2+x3)/2 + (1 x x1)/2+1 = (x1+x2+x3)/3
y = 2x(y2+y3)/2 + (1 x y1)/(2+1) = (y1+y2+y3)/3
Hence, the coordinates of the centroid are given by
x = (x1+x2+x3)/3, y = (y1+y2+y3)/3.

Directions: Solve the following.
Q 1: Find the centroid of the triangle whose angular points are (3, -5), (-7, 4) and (10, -2) respectively.
(2, -1)
(-2, 1)
(2, 1)
(-2, -1)

Q 2: Find the centroid of the triangle whose angular points are (-1,0), (5, -2) and (8, -2)
(0, -4)
(-4,0)
(0, 4)
(4, 0)

Q 3: The vertices of a triangle are (1,2), (h, -3) and (-4, k). FInd the values of h and k if the centroid of the triangle be at the point (5, -1).
(18, -2)
(-18, -2)
(2, 18)
(8, 2)

Q 4: Find the third vertex of a triangle if two of its vertices are at (-1,4) and (5,2)
(-4, -15)
(-4, 15)
(4, -15)
(4, 15)

Q 5: If (2,4) is the centroid of the triangle two of whose vertices are (7,1) and (2,7). Find the remaining vertex.
(3,4)
(-3,-4)
(-3,4)
(3,-4)

Q 6: Origin is the centroid of the triangle, whose two vertices are (5, -1), (-2,3).Find the third vertex.
(3,-2)
(3, 2)
(-3, -2)

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Question 8: This question is available to subscribers only!


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