Centroid Formula

Q.

If two vertices of a triangle are (6, 4), (2, 6) and its centroid is (4, 6), then the third vertex is

1. (4, 8)

2. (0, 0)

3. (8, 4)

4. (6, 4)

Q.

The centroid of a triangle whose vertices are (3, 0), (7, 0) and (8, 6) is

1. (6, 2)

2. (4, 3)

3. (0, 0)

4. (2, 6)

Q.

The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).

1. $\sqrt{6}\text{units}$

2. $\sqrt{3}\text{units}$

3. $\sqrt{2}\text{units}$

4. $\sqrt{5}\text{units}$

Q.

If A(4, -3), B(3, -2) and C(2, 8) are the vertices of a triangle, then its centroid will be

1. (-3, 3)

2. (3, 3)

3. (3, 1)

4. (1, 3)

Q.

The orthocentre of the triangle with vertices
$(2,\frac{\sqrt{3}-1}{2}),(\frac{1}{2},-\frac{1}{2})and(2,-\frac{1}{2})$ is

1. $(2,-\frac{1}{2})$

2. $(\frac{5}{4},\frac{\sqrt{3}-2}{4})$

3. $(\frac{1}{2},-\frac{1}{2})$

4. $(\frac{3}{2},\frac{\sqrt{3}-3}{6})$

Q. Find the co-ordinates of the centroid of the triangle whose vertices are (3, -5) , (4, 3) , (11, -4).

1. (4 , -3)
2. (-6 , 3)
3. (3 , -2)
4. (6 , -2)

Q. In $△$ABC , G(-4, -7) is the centroid. If the coordinates of A and B are (-14, -19) and (3, 5) respectively, then find the co-ordinates of C.

1. (-1, 7)
2. (-1, -7)
3. (-2, -7)
4. (1, 7)

Q. Find the co-ordinates of the centroid of the triangle whose vertices are (4, 7) , (8, 4) & (7, 11).

1. $(\frac{17}{3},\frac{19}{3})$
2. $(\frac{11}{3},\frac{19}{3})$
3. $(\frac{19}{3},\frac{22}{3})$
4. $(\frac{22}{3},\frac{22}{3})$

Q. A(h, -6) , B(2, 3) and C(-6, k) are co-ordinates of vertices of a triangle whose centroid is G(1, 5). Find the values of h and k.

1. h = 5 and k = -7
2. h = 18 and k = -7
3. h = -7 and k = 18
4. h = 7 and k = 18

Q.

What will be the centroid of a triangle whose vertices are (2, 4), (6, 4) and (2, 0)?

1. $\frac{8}{3},\frac{5}{3}$
2. $\frac{7}{2},\frac{5}{2}$
3. $\frac{10}{3},\frac{8}{3}$
4. $\frac{4}{3},\frac{2}{3}$