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

Answer :

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 (x_{3}, y_{3}).

And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x_{1}, y_{1}) and (x_{2}, y_{2}) is

(where, (x_{1}, y_{1}) and (x_{2}, y_{2}) are the coordinates of P and R

Now, Let the co-ordinates of mid-point of QS be (x_{4}, y_{4}).

And, since it is a mid-point –

(where, (x_{5}, y_{5}) and (x_{6}, y_{6}) are the coordinates of Q and S.

And, since it is a parallelogram –

⇒ x_{4} = x_{3} and y_{4} = y_{3}

⇒ x = 2 and y = 3.

Rate this question :

The co-ordinates of vertices of A, B, C of a triangle ABC are (–1, 3), (1, –1) and (5, 1) respectively, let us calculate the length of Median AD.

West Bengal MathematicsThe mid-point of line segment joining two point s (ℓ, 2m), and (–ℓ + 2m, 2ℓ – 2m) is

West Bengal MathematicsThe co-ordinates of end point s of a diameter of a circle are (7, 9) and (–1, –3). The co-ordinates of centre of circle is

West Bengal MathematicsThe point P lies on the line segment AB and AP = PB; the co-ordinates of A and B are (3, –4) and (–5, 2) respectively. Let us write the co-ordinates of point ?

West Bengal MathematicsThe abscissa at the point P which divides the line segment joining two point s A(1, 5), B(–4, 7) internally in the ratio 2: 3 is

West Bengal MathematicsProve that when the point s A (7, 3), B (9, 6), C (10, 12) and D (8, 9) are joined in order, then they will form a parallelogram.

West Bengal Mathematics