Q. 11 E4.0( 11 Votes )
If the point s P(1, 2), Q(4, 6), R(5, 7) and S(x, y) are the vertices of a parallelogram PQRS, then
A. x = 2, y = 4
B. x = 3, y = 4
C. x = 2, y = 3
D. x = 2, y = 5
P(1, 2), Q(4, 6), R(5, 7) and S(x, y) We know that a quadrilateral is a parallelogram if the co-ordinates of mid-point s of its both the diagonals are same.
Therefore, we’ll use the mid-point s of diagonal PR and QS.
Let the co-ordinates of mid-point of PR be (x3, y3).
And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x1, y1) and (x2, y2) is
(where, (x1, y1) and (x2, y2) are the coordinates of P and R
Now, Let the co-ordinates of mid-point of QS be (x4, y4).
And, since it is a mid-point –
(where, (x5, y5) and (x6, y6) are the coordinates of Q and S.
And, since it is a parallelogram –
⇒ x4 = x3 and y4 = y3
⇒ x = 2 and y = 3.
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