Centroid

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. A straight rod of length 3l units slides with its ends A, B always on the x and y axes respectively then the locus of centroid of $△OAB$ is

1. 
2. 
3. 
4. 

Q. For $△ABC$ whose vertices are given by $A(3,6),B(-4,7)$ and $C(10,-7),$ if $A_1,B_1,C_1$ represent the mid points of sides opposite to vertices $A,B,C$ respectively, of $△ABC$ and $A_2,B_2,C_2$ represent the mid points of sides opposite to vertices $A_1,B_1,C_1$ respectively, of $△A_1{B}_1{C}_1$ and so on, then which of the following is/are correct?

1. $\frac{\text{Area (}△A_2{B}_2{C}_2\text{)}}{\text{Area (}△ABC\text{)}}=\frac{1}{16}$
2. $\frac{\text{Area (}△A_3{B}_3{C}_3\text{)}}{\text{Area (}△ABC\text{)}}=\frac{1}{16}$
3. The centroid of $△A_3{B}_3{C}_3$ is $(3,2)$
4. The centroid of $△A_2{B}_2{C}_2$ is $(3,2)$

Q.

If the vertices of a triangle be (a, b - c), (b, c - a) and (c, a - b), then the centroid of the triangle lies

1. At origin

2. On x-axis

3. None of these

4. On y-axis

Q.

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

1. (0, 0)

2. (8, 4)

3. (6, 4)

4. (4, 8)

Q. Let $O(0,0),P(3,4),Q(6,0)$ be the vertices of the triangle OPQ. The point R inside the tringle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

1. $(\frac{4}{3},3)$
2. $(3,\frac{2}{3})$
3. $(3,\frac{4}{3})$
4. $(\frac{4}{3},\frac{2}{3})$
   

Q. Let A (2, -3) and B(-2, 1) be the vertices of a tirangle ABC. If the centroid of this triangle moves on the line $2x+3y=1,$ then the locus of the vertex C is the line

1. 2x+3y=9
2. 5x-3y=7
3. 3x-2y=3
4. 3x+2y=5

Q. Two vertices of a triangle are (3, -5) and (-7, 4). If the centroid of the triangle is (2, -1), then the coordinates of the third vertex are .

1. (10, -2)
2. (-10, -2)
3. (10, 2)
4. (-10, 2)

Q. One vertex of the equilateral triangle with centriod at origin and one side as $x+y-2=0$ is

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

Q. A point $P$ moves on the line $2x-3y+4=0$. If $Q(1,4)$ and $R(3,-2)$ are fixed points, then the locus of the centroid of $\Delta PQR$ is a line :

1. parallel to x-axis
2. with slope $\frac{3}{2}$
3. parallel to y-axis
4. with slope $\frac{2}{3}$