The Coordinates of Centroid

Q. ABC is a triangle whose vertices are A (3, 4), B (-2, -1) and C (5, 3). If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

1. (2, 7)
2. (1, 0)
3. (5, -6)
4. (-7, 9)

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

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

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

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

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

Q. ABC is a triangle whose vertices are A (3, 4), B (-2, -1) and C (5, 3). If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

1. (2, 7)
2. (1, 0)
3. (5, -6)
4. (-7, 9)

Q. The centroid of a triangle is given as C(a, 3b) having vertices A(-a, 2b), B(-2a, 4b) and C(x, y).the values of x and y are

1. 6a and 6b
2. 3a and 3b
3. 3a and 6b
4. 6a and 3b

Q.

ABC is a triangle whose vertices are A(3, 4), B(-2, -1) and C(5, 3). If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

Q. In a triangle, centroid is the point of intersection of

1. perpendicular bisector.
2. medians.
3. angular bisector.
4. altitudes.

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, 1)

3. (1, 3)

4. (-3, 3)

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. (6, 4)

3. (8, 4)

4. (0, 0)

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. (-2, -7)
3. (1, 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. $(\frac{22}{3},\frac{22}{3})$
4. $(\frac{19}{3},\frac{22}{3})$

Q. If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then $a^3+b^3+c^3$ is equal to

1. abc
2. 0
3. a+b+c
4. 3abc

Q.

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

1. (2, 6)

2. (4, 3)

3. (6, 2)

4. (0, 0)

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)