Practice the questions given in the worksheet on finding the centroid of a triangle. We know the centroid of a triangle is the point of intersection of its medians and it divides each median in the ratio 2 : 1.
1. Calculate the coordinates of the centroid of the triangle ABC, if A = (7, 2), B = (0, 1) and C = (1, 4).
2. Find the centroid of the triangle PQR whose vertices are P(1, 0), Q(5, 2) and R(8, 2).
3. Let the vertices of a triangle be A (1, 2), B (2, 5) and C (2, 1). Find its centroid and the length of the median through C.
4. The centroid of a triangle ABC is (1, 1). Two of the vertices are A (3, 4), B (4, 7). Find the coordinates of the third vertex.
5. Find the coordinates of the centroid of a triangle PQR whose vertices are P (6, 2), Q (4, 3) and R (1, 4).
6. Two vertices of a triangle are (1, 3) and (2, 4). If the origin is the centroid of the triangle, find the third vertex.
7. If G (2, 1) is the centroid of a triangle PQR and two of its vertices are P (1, 6) and Q (5, 2), find the third vertex of the triangle.
8. In the triangle ABC, AD is a median. If A (5, 3) and D (1, 9) then find the centroid of the triangle ABC.
9. Find the third vertes of a triangle PQR if two of its vertices are Q (3, 1) and R (0, 2), and its centroid is at the origin.
10. P (3, 2) and Q (2, 1) are the two vertices of the triangle PQR, whose centroid is G (\(\frac{5}{3}\), \(\frac{1}{3}\)). Find the coordinates of the third vertex R.
11. Let the vertices of a triangle be (4, 1), (3, 4) and (1, 3). Prove that its centroid in the origon.
12. The coordinates of the centroid of a triangle PQR are (2, 5). If Q = (6, 5) and R = (11, 8); calculate the coordinates of the vertex P.
Answers for the worksheet on centroid of a triangle are given below:
Answers:
1. (2, 1)
2. G (4, 0)
3. (\(\frac{1}{3}\), \(\frac{2}{3}\)); \(\frac{5}{2}\)√2 units
4. (4, 0)
5. G (3, 3)
6. (3, 1)
7. R (2, 7)
8. (\(\frac{7}{3}\), 5)
9. P (3, 1)
10. R (4, 4)
12. (1, 28)
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