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 - Mathematics

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

(a) (6, 3)

(b) (3, 6) 

(c) (5, 6)

(d) (1, 4)



(a) (6, 3)

Explanation:




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`

Now,

Comparing the co-ordinates,

= `"x + 1"/2` = `"3 + 4"/2`

= `"x + 1"/2` = `"7"/2`

= (1 + x) = 7

= x = (7-1)

= x = 6


Similarly,

= `"6 + 2"/2` = `"5 + y"/2`

= 4 = `"5 + y"/2`

= 4 x 2 = 5 + y

= 8 = 5 + y

= y = 8 - 5

= y = 3

∴ (x,y) = (6,3)

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CBSE Class 10 Mathematics Sample Paper-2022