If A (1,2), B (4, y), C (x,6) and D (3,5) are vertices of a parallelogram ABCD, find the values of x and y. [4 MARKS]
Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks
Consider a parallelogram ABCD .
Let O be the point of intersection of the diagonals AC and BD
We know that diagonals of a parallelogram bisect each other.
⇒ O is the midpoint of both the digonals AC and BD
Now, coordinates of O as mid-point of BD are
O(x,y)=(x1+x22),(y1+y22)
⇒O(a,b)=4+32,y+52……(1)
Also, coordinates of O as mid-point of AC are
O(a,b)=1+x2,2+62……(2)
From (1) and (2), we have
4+32=1+x2
72=1+x2⇒x=6
And y+52=2+62
y+52=82⇒y=3