Question

(4, 2) and (-1, 5) are the adjacent vertices ofa parallelogram. (-3, 2) are the coordinates of the points of intersection of its diagonals. Find the coordinates of the other two vertices. 

Answer 1

Let the coordinates of C and D  be (x, y) and (a , b) respectively.

Midpoint of AC is O coordinates of O are ,

O (-3 , 2) = O `((4 + "x")/2 , (2 + "y")/2)`

`-3 = (4 + "x")/2 ,   2 = (2 + "y")/2`

- 6 = 4 + x  , 4 = 2 + y

x = - 10 , y = 2

C (-10 , 2)

Similarly , coordinates of midpoint of DB , i.e. O are ,

O (-3 , 2) = O `(("a" - 1)/2 , ("b" + 5)/2)`

`-3 = ("a" - 1)/2 ,   2 = ("b" + 5)/2`

- 6 = a - 1 , 4 = b + 5

a = -5 , b = -1

D (- 5 , -1)

Thus , the coordinates of each other two vertices are (-10 , 2) and (-5 - 1)