1.

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

Answer»

Answer:

x = 6

y = 3

Step-by-step explanation:

ABCD is a parallelogram with vertices  (1,2) ; (4,y) ; (x,6) ; (3,5) respectively.

As we know,

The mid-points of TWO diagonals MUST be same.

So, we will apply 'mid-point rule'

mid-point of AC is given by \frac{1+x}{2} , \frac{2+6}{2} = ( \frac{1+x}{2} , \frac{8}{2} )

mid-point of BD is given by \frac{3+4}{2} , \frac{5+y}{2} = ( \frac{7}{2} , \frac{5+y}{2} )

Now, mid-point of AC = mid-point of BD

1+x/2  = 7/2

x = 7-1

x = 6 //

5+y/2 = 4

y = 8-5

y = 3//

∴ x = 6, y = 3

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