If the points A(6, 1), B(8, 2), C(p, 4) and D(7, 3) are the vertices of a parallelogram,
taken in order, find the value of p.
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Answer:
We know that the diagonals of a parallelogram bisect each other. So, coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.
∴(
2
6+9
,
2
1+4
)=(
2
8+p
,
2
2+3
)
⇒(
2
15
,
2
5
)=(
2
8+p
,
2
5
)
⇒
2
15
=
2
8+p
⇒15=8+p⇒p=7
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