Question

If (7,3), (6,1), (8,2) and (P,4) are the vertices of a parallelogram taken in order then the value of P is-
A. 4
B. 6
C. 7
D. 9

Answer 1

Hint: To solve such questions we need to remember the property that the diagonals of the parallelogram bisect each other.

Complete Step-by-Step solution:

A(7,3), B(6,1), C(8,2) and D(P,4)
Since we know that the diagonals of a parallelogram bisect each other therefore the coordinates of the point O can be found using opposite coordinates as A and C, which are
X coordinate=$\dfrac{{7 + 8}}{2} = \dfrac{{15}}{2}$

=7.5
Y coordinate=$\dfrac{{3 + 2}}{2} = \dfrac{5}{2}$
=2.5
Hence the X coordinate of point must also satisfy the X coordinate of point O.
$7.5 = \dfrac{{P + 6}}{2}$
$
  15 = P + 6 \\
  P = 9 \\
$

Note: The following such question can easily be solved by using the basic properties of parallelogram. As we should remember that the diagonals of a parallelogram bisect each other. Proceeding like this you will get the right answer.