Question

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.

Solution

Correct option is

 

Let the coordinates of A be (α, β) 

then coordinates of B are (8 – α, 10 – β)      

and coordinates of C are (8 – α, –6 – β) 

∵ D is the mid point of BC then  

       

  

∴ Coordinates of ABC are (10, –1), (–2, 11) and (–2, –5) respectively. 

Now coordinates of centriod  

        

   

              

      

                

       

             

Hence, 

            

                                                       

                                                       

SIMILAR QUESTIONS

Q1

Determine the ratio in which y – x + 2 = 0 divides the line joining (3, –1) and (8, 9).

Q2

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (–1, 2) and (2, 5). Then find the coordinates of the fourth vertex.

Q3

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.

Q4

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

Q5

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.

Q6

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.

Q7

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

Q8

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

Q9

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).

Q10

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