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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