Question

The vertices of a parallelogram in order are A(1, 2), B(4, y), C(x, 6) and D(3, 5). Then (x, y) is ______.

पर्याय

• (6, 3)

• (3, 6)

• (5, 6)

• (1, 4)

Answer 1

The vertices of a parallelogram in order are A(1, 2), B(4, y), C(x, 6) and D(3, 5). Then (x, y) is (6, 3).

Explanation:-

Since ABCD is a parallelogram, diagonals AC and BD bisect each other

∴ mid point of AC = mid point of BD

`((x+1)/2,(6+2)/2)=((3+4)/2,(5+y)/2)`

Comparing the co-ordinates, we get,

`(x+1)/2=(3+4)/2`

So, x = 6

Similarly, `(6+2)/2=(5+y)/2`

So, y = 3

∴ (x, y) = (6, 3)