Centroid Formula

Q.

Find the centroid of a triangle, whose vertices are $\left(3,-5\right),\left(-7,4\right)$ and $\left(10,2\right)$.

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.

The two opposite vertices of a square are $(-1,2)$ and $(3,2)$. Find the coordinates of the other two vertices.

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.

A(2, 4) and B(8, 12) are two ends of a line segment. Find the point which divides AB internally in the ratio 1:3.

1. (3.75, 5)

2. (3, 6.5)

3. (3.5, 6)

4. (3, 6)

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. The locus of the mid points of the chords of the circle $x^2+y^2+2x-2y-2=0$ which makes an angle of $90°$ at the centre is

1. $x^2+y^2-2x-2y=0$
2. $x^2+y^2-2x+2y=0$
3. $x^2+y^2+2x-2y=0$
4. $x^2+y^2+2x-2y-1=0$

Q. In $\Delta ABC$ if orthocentre be $(1,2)$ and circumcentre be $(0,0)$, the centroid of $\Delta ABC$ is

1. $(\frac{1}{2},\frac{2}{3})$
2. $(\frac{1}{3},\frac{2}{3})$
3. $(\frac{2}{3},1)$
4. none of these

Q. If the centriod of a triangle formed by points $(a,b),(b,c)$ and $(c,a)$ is $(0,0)$, then find $a^3+b^3+c^3$.

Q. Find the coordinates of centroid of the triangles with vertices:
$(-1,3),(6,-3)$ and $(-3,6)$

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. A triangle has a base measuring 15 cm and a height of 16 cm. Calculate its area.

1. 130
2. 120
3. 140
4. 150

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.

Q.

If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

Q. If $\theta$ is parameter, $A=(a\sec \theta ,b\tan \theta )andB=(-a\tan \theta ,b\sec \theta ),O=(0,0)$ then the locus of the centroid of $△OAB$ is

1. $9xy=ab$
2. $xy=9ab$
3. $x^2-9y^2=a^2-b^2$
4. $x^2-y^2=\frac{1}{9}(a^2-b^2)$

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. Question 3 (iv)
The points $A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)$ are the vertices of $\Delta$ ABC. What are the coordinates of the centroid of the triangle ABC?

Q. The coordinates of the mid points of the sides of a triangle are (3, 1), (2, 3) and $(-2,2)$. Find the coordinates of the centroid of the triangle ABC.

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. Find the centroid of $△ABC$ whose vertices are A(-3, 0), B(5, -2) and C(-8, 5).

Q. Mid-points of the sides $AB$ and $AC$ of a $△ABC$ are $(3,5)$ and $(-3,-3)$ respectively, which of the following is the length of the side $BC$?

1. $10units$
2. $15units$
3. $30units$
4. $20units$

Q. The sum of the three altitudes of a triangle is $......$ than its perimeter

1. Less
2. Equal
3. More
4. Less than or more than

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.

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. $\frac{4}{3},\frac{2}{3}$

Q. If $\theta$ is parameter, $A=(a\cos \theta ,a\sin \theta )$ and $B=(b\sin \theta ,-b\cos \theta )$ , $C=(1,0)$ then the locus of the centroid of $\Delta ABC$ is

1. $(3x+1{)}^2+9y^2=a^2+b^2$
2. $(3x-1{)}^2+9y^2=a^2-b^2$
3. $(3x-1{)}^2+9y^2=a^2+b^2$
4. $(3x+1{)}^2+9y^2=a^2-b^2$

Q. Find the coordinates of the point equidistant from three given points $A(5,3),B(5,-5)$ and $C(1,-5)$.

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

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

Q. Find the Centroid of the triangle with vertices $A(3,-7),B(5,1)$ and $C(-1,-5)$