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 co-ordinates 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 co-ordinates 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 co-ordinates 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 co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates 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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