Question

The diagonal AC and BD of a parallelogram ABCD intersect at O.if OA=2x-3,OC=y+4,OB=x+3 and OD=2y-1, find the values of x and y.

Answer 1

Answer:

x = 6 ; y = 5

Step-by-step explanation:

Diagonals of a parallelogram, bisect each other.

Here, O is the point of intersection.

So, OA = OC and OB = OD

2x - 3 = y + 4

2x - y = 7...(i) and

x + 3 = 2y - 1

x - 2y = -4....(ii)

Solving equations (i) and (ii) using (i) - 2×(ii) we get,

2x - y - 2x + 4y = 7 + 8

3y = 15

y = 5 and

x - 2×5 = -4

x = 6

Hence, x = 6 and y = 5.