Question

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.

Solution

Correct option is

(4, 6)

 

Let the fourth vertex be . Since ABCD is a parallelogram, the diagonals bisect to each other.           

i.e., mid point of BD = mid point  of AC

 

on equating abscissaes and cordinates, we get 

             

Hence the coordinates of the fourth vertex 

SIMILAR QUESTIONS

Q1

Transform the equation  into cartesian form.

Q2

Transform the equation  into polar form.

Q3

 

Find the distance between the points

            

where a > 0.

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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.