Centroid

Q.

Two vertices of $△ABC$ are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are

(a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)

Q.

The point of intersection of all the medians of a triangle is called the ___ of the triangle.

1. centroid

2. incentre

3. circumcentre

4. orthocentre

Q.

The point of intersection of all the medians of a triangle is called the

1. incentre

2. centroid

3. orthocentre

4. circumcentre

Q.

What is the relation between orthocentre, circumcentre, and centroid?

Q.

In what ratio does the median of a triangle divide its sides? 1 : __

__

Q.

$ABC$ is a triangle with vertices $A(-1,4),B(6,-2)\&c(-2,4)$, $D,\hspace{0.17em}E\&F$are the points which divide each $AB,BC\&CA$, internally in the ratio $3:1$. Then, the centroid of $△DEF$ is

1. $(3,6)$

2. $(1,2)$

3. $(4,8)$

4. $(-3,6)$

5. None of the above

Q. Why the ratio of median is 2:1?

Q. Prove that the centroid of any triangle is same as the centroid of the new triangle formed by joining the mid point of its sides

Q. A centroid divides the median in the ratio of 2:1 .

1. True
2. False

Q.

You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, − 6), B (3, − 2) and C (5, 2)

Q.

If A(-1, 0), B(5, -2) and C(8, 2) are the vertices of a $△ABC$ then its centroid is

(a) (12, 0) (b) (6, 0) (c) (0, 6) (d) (4, 0)

Q.

In the above triangle ABC, point P is the centroid of the triangle. The length of AE is 15 cm. Find the length of AP and PE.

1. AP = 10 cm, PE = 5 cm

2. AP = 9 cm, PE = 6 cm

3. AP = 8 cm, PE = 7 cm

4. AP = 5 cm, PE = 10 cm

Q.

Find the coordinates of the centroid of a $\Delta ABC$ whose vertices are

A(5, 10), B (10, 0), C(5, 4)

1. (4, -5)

2. $(\frac{20}{3},8)$

3. $(\frac{20}{3},-8)$

4. (6, 9)

Q.

Find the third vertex of a $△ABC$ if two of its vertices are B(-3, 1) and C(0, -2), and its centroid is at the origin.

Q.
In the above triangle ABC, point P is the centroid of the triangle. The length of AE is 15 cm. Find the length of AP and PE.

Q. Is centroid always dividing the median of any triangle in the ratio 2:1 if yes then prove it

Q. Find the length of the medians of a ΔABC having vertices at A(0, −1), B(2, 1) and C(0, 3).

Q.

In the given triangle ABC, the point P is the intersection of all the medians. The length of AE is 24 cm. Then what is the length of AP?

1. 8 cm

2. 10 cm

3. 12 cm

4. 16 cm

Q.

In the given triangle ABC, the point P is the intersection of all the medians. The length of AP is 10 cm. Then what is the length of PE?

1. 2 cm

2. 5 cm

3. 20 cm

4. 15 cm

Q.

In triangle ABC shown below, point G is the intersection of all the medians. If the length of AP is 18 cm, then the length of AG and GP respectively are:

1. 10, 5 cm

2. 9, 6 cm

3. 12, 6 cm

4. 5, 10 cm

Q.

Co-ordinates of the centroid of a triangle whose vertices are

P(-1, 2), Q(1, -1) and R(6, 1) are .

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

Q. Two vertices of a triangle are $A(1,1),B(2,-3)$. If its centroid is $(2,1)$, find the third vertex.

1. $(3,5)$
2. $(3,-5)$
3. $(-3,5)$
4. $(4,5)$

Q. Find the third vertex of triangle, if two of its vertices are $(5,7)$ and $(0,3)$ and centroid at origin.

1. $10,5$
2. $5,10$
3. $-5,-10$
4. $-10,-5$

Q. The equation of second degree $x^2+2\sqrt{2}xy+2y^2+4x+4\sqrt{2}y+1=0$ represents a pair of straight lines, the distance between them is?

1. $3$
2. $2\sqrt{3}$
3. $4$
4. $4\sqrt{3}$

Q.

If the vertices of a triangle are (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. On y-axis

4. None of these

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

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

Q. The centroid of the triangle whose vertices are A(4, -6), B(3, -2) and C(5, 2) is

1. 4 , 3
2. 3, 2
3. 4, 1
4. 4, -2

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

Q. The centroid of a triangle formed by $(7,p),(q,-6),(9,10)$ is $(6,3)$, then find $p+q$.

Q. The vertices of a triangle are $(2,1),(5,2)$ and $(3,4)$. Then the co-ordinates of the centroid are

1. $(10,3)$
2. $(\frac{10}{3},7)$
3. $(\frac{10}{3},\frac{7}{3})$
4. $(\frac{7}{3},\frac{10}{3})$