Question

 

 are mid points of the sides of a triangle, then find

(i) Centroid of the triangle 

(ii) Incentre of the triangle

Solution

Correct option is

 

Let , then coordinates of  and coordinates of . But mid point of BC is 

       

  

  

  

∴ Coordinates of vertices are  

       

(i) Centroid : The centriod of ∆ABC is

                

    

  

(ii) Incentre : We have  

         

         

and, 

         

  

          

  

.

SIMILAR QUESTIONS

Q1

The mid points of the sides of a triangle are (1, 2), (0, –1) and (2, –1). Find the coordinates of the vertices of a triangle with the help of two unknowns.

Q2

Find the coordinates of a point which divides externally the line joining (1, –3) and (–3, 9) in the ratio 1: 3.

Q3

The line segment joining A(6, 3) to B(–1, –4) is doubled in length by having its length added to each end. Find the coordinates of the new ends.

Q4

Find the ratio in which the point (2, y) divides the line segment joining (4, 3) and (6, 3) and hence find the value of y.

Q5

Find the harmonic conjugates of the point R(5, 1) with respect to the points P(2, 10) and Q(6, –2).

Q6

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Q7

The vertices of a triangle are (1, 2), (h, –3) and (–4, k). Find the value of . If the centroid of the triangle be at the point (5, –1).

Q8

If D(–2, 3), E(4, –3) and F(4, 5) are the mid points of the sidesBCCA and AB of triangle ABC, then find   where G is the centroid of ∆ABC.

Q9

Find the coordinates of incentre of the triangle whose vertices are (4, –2), (–2, 4) and (5, 5).

Q10

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21),C(7, –3), D(12, 2) and E(0, –3).