Question

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

Solution

Correct option is

(–4, –15)

 

Let the third vertex be (xy) then the coordinates of the centroid of triangle are   

            

  

     

  

  

Hence the third vertex is (–4, –15). 

Short Cut Method :

According to corollary 2 :  

        

                    = (–4, –15).

SIMILAR QUESTIONS

Q1

Find the coordinates of the point which divides the line segment joining the points (5, –2) and (9, 6) in the ratio 3 : 1.

Q2

Find the length of median through A of a triangle whose vertices are A(–1, 3), B(1, – 1)and C(5, 1).

Q3

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

Q4

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.

Q5

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.

Q6

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

Q7

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.

Q8

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.

Q9

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

Q10

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).