Question

If (1,2), (4, y), (x, 6) and (3,5) are the vertices of a parallelogram taken in order, find x and y​

Answer 1

ANSWER

Let A(1,2), B(4,y),C(x,6) and D(3,5) are the vertices of a parallelogram ABCD

.AC and BD are the diagonals .

O is the midpoint of AC and BD.

If O is the mid-point of AC ,then the coordinates of O are =(

2

1+x

,

2

2+6

)=(

2

x+1

,4)

If O is the mid-point of BD then coordinates of O are (

2

4+3

,

2

5+y

)=(

2

7

,

2

5+y

)

Since both coordinates are of the same point O

∴

2

1+x

=

2

7

⇒1+x=7

⇒x=7−1=6

∴

2

5+y

=4

⇒5+y=8

⇒y=8−5=3

Hence x=6 and y=3.