Q. 64.2( 323 Votes )

# If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Answer :

Let (1, 2), (4, *y*), (*x*, 6), and (3, 5) are the coordinates of A, B, C, D vertices of a parallelogram ABCD.

Intersection point O of diagonal AC and BD also divides these diagonals.

Therefore, O is the mid-point of AC and BD.

By mid point formula, If (x, y) is the midpoint of the line joining points A(x

_{1}, y

_{1}) and B(x

_{2}, y

_{2}) Then,

If O is the mid-point of AC, then the coordinates of O are:

() = (, 4)

If O is the mid-point of BD, then the coordinates of O are:

(, ) = (, )

Since both the coordinates are of the same point O

Comparing the x coordinates we get,

x + 1 = 7

x = 6

And,

Comparing the y coordinates we get,= 4

5 + y = 8

y = 3

Hence, x = 6 and y = 3.

Rate this question :

If A(1,5), B (-2,1) and C(4,1) be the vertices of ΔABC and the internal bisector of ∠A meets BC and D, find AD.

KC Sinha - MathematicsThe line segment joining A(6,3) to B(-1,-4) is doubled in length by having half its length added to each end. Find the coordinates of the new ends.

KC Sinha - MathematicsIf the points (10,5),(8,4) and (6,6) are the mid-points of the sides of a triangle, find its vertices.

KC Sinha - MathematicsThe line segment joining A (2,3) and B(-3,5) is extended through each end by a length equal to its original length. Find the coordinates of the new ends.

KC Sinha - MathematicsIf the middle point of the line segment joining (3,4) and (k,7) is (x,y) and 2x+2y+1=0, find the value of k.

KC Sinha - Mathematics