Centroid

Q. Which of the following options have their centroid outside the triangle?

1. None of the above
2. 
3. 
4. 

Q.

$A(-1,3),B(4,2)andC(3,-2)$ are the vertices of a triangle .

(i) Find the coordinates of the centroid $G$ of the triangle.

(ii) Find the equation of the line through $G$ and parallel to $AC$.

Q. In a $\Delta$ABC D, E, F are midpoints of sides BC, AC, AB respectively. If D, E, F are joined to A, B, C respectively to meet at a common point G, then select the correct options.

1. There are 6 triangles formed with G as one of the vertex.
2. G is the centroid of the triangle.
3. GD is a part of median.
4. BGC is a triangle.

Q.

The point of intersection of medians is called ___.

1. circumcentre

2. incentre

3. centroid

4. orthocentre

Q.

Find the third vertex of a triangle if its two vertices are
(-1, 4) and (5, 2) and mid-point of one side is (0, 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. 5x-3y=7
2. 3x+2y=5
3. 2x+3y=9
4. 3x-2y=3

Q. The third vertex of a triangle, whose two vertices are $(-4,1)$ and $(0,-3)$ and centroid is at the origin is

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

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. $A(1,4)andB(6,-3)$ are two vertices of ABC and C is a point on the locus $5x+4y=9$. Find the equation of the locus of the centroid of $\Delta ABC$.

Q. If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify.
[3 marks]