#### Question

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

#### Solution

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.

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

`((1+x)/2,(2+6)/2) => ((x+1)/2, 4)`

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

`((4+3)/2,(5+y)/2)=>(7/2, (5+y)/2)`

Since both the coordinates are of the same point O,

`:. (x+1)/2 = 7/2 `

⇒ x+1 =7 and 5+y = 8

⇒ x = 6 and y = 3

Is there an error in this question or solution?

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