Different types of questions are given under the worksheet on centroid of a triangle.
Let us recall the formula for finding the centroid of a triangle as follows;
The coordinates of the centroid of the triangle formed by joining the points (x₁, y₁) , (x₂, y₂) and (x₃, y₃) are
({x₁ + x₂ + x₃}/3 , {y₁ + y₂ + y₃}/3
To learn more about how to find the centroid of a triangle Click Here.
Here two varieties of questions are given:
(i) using the formula to find the centroid of a triangle where three vertices are given
(ii) for finding the third vertex where centroid of a triangle is given along with the coordinates of its two vertices
1. Find the coordinates of the centroid of the triangle formed by the following sets of three points:
(i) (7, 5), ( 2, 5) and (4, 6)
(ii) (4,  1), (0, 3) and ( 4,  2)
(iii) (3,  4), (4, 7) and (2, 9) .
2. Show that the origin is the centroid of the triangle formed by the points (x  y, y  z),( x,  y) and (y, z).
3. Find the coordinates of the point of intersection of the medians of the triangle formed by joining the points (1,  2), (8, 4) and (5, 7).
4. The coordinates of the vertices of a triangle are (4,  3), ( 5, 2) and (x, y). If the centre of gravity of the triangle is at the origin find x, y.
5. The centroid of a triangle is ( 1,  2) and coordinates of its two vertices are (4, 6) and ( 8,  12). Find the coordinates of its third vertex.
6. The coordinates of the vertex A of the ∆ ABC are (2, 5); if the centroid of the triangle is at (2, 1), find the coordinates of the midpoint of the side BC.
Answers for the worksheet on centroid of a triangle are given below to check the exact answers of the above questions on midpoint.
1. (i) (3, 2)
(ii) (0, 0)
( iii) (3, 4)
3. (4, 3)
4. x = 1 , y = 1
5. (1, 0)
6. (4, 1)
● Coordinate Geometry
11 and 12 Grade Math
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