Question

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.

Solution

Correct option is

(1, – 4), (3, 2) and (–1, 2)

 

Let D (1, 2), E(0, –1) and F(2, –1) be the mid points of BCCAand AB respectively. 

Let the coordinates of A be  then coordinates of B and C are  respectively

D is mid point of B and C.                 

  

  

  

  

Hence coordinates of AB and C are (1, – 4), (3, 2) and (–1, 2) respectively.

SIMILAR QUESTIONS

Q1

Transform the equation  into polar form.

Q2

 

Find the distance between the points

            

where a > 0.

Q3

An equilateral triangle has one vertex at the point (0, 0) and another at . Find the coordinates of the third vertyex. 

Q4

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

Q5

Find the circumcentre of the triangle whose vertices are (–2, –3), (–1, 0) and (7, –6). Also find the radius of the circumcircle.

Q6

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

Q7

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

Q8

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

Q9

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.

Q10

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