If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
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Let A(1,2), B(4,y),C(x,6) and D(3,5) are the vertices of a parallelogram ABCD
.AC and BD are the diagonals .
O is the midpoint of AC and BD.
If O is the mid-point of AC ,then the coordinates of O are =(
2
1+x
,
2
2+6
)=(
2
x+1
,4)
If O is the mid-point of BD then coordinates of O are (
2
4+3
,
2
5+y
)=(
2
7
,
2
5+y
)
Since both coordinates are of the same point O
∴
2
1+x
=
2
7
⇒1+x=7
⇒x=7−1=6
∴
2
5+y
=4
⇒5+y=8
⇒y=8−5=3
Hence x=6 and y=3.
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