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Question

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]


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Solution

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+x2x=6

And y+52=2+62

y+52=82y=3


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