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(x1, y1) and B(x2, y2) 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