Question

(-2,-1),(1,0),(x,3),(3,y) form a parallelogram find the values of x and y.

Answer 1

value of x = 6 and y = 2

(-2,-1), (1,0), (x,3) and (3,y) form a parallelogram.

we know, diagonals of parallelogram

diagonals of parallelogram concide at a same point.

if A = (-2, -1) , B = (1, 0) , C = (x , 3) and D = (3, y)

then, midpoint of diagonal AC = midpoint of diagonal BD

⇒[(-2 + x)/2 , (-1 + 3)/2 ] = [(1 + 3)/2, (0 + y)/2 ]

⇒[(-2 + x)/2 , 1 ] = [2, y/2 ]

so, (-2 + x)/2 = 2 ⇒x = 6

⇒1 = y/2 ⇒y = 2

hence, x = 6 and y = 2

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