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

**Solution:**

The coordinates of the point P(x, y) which divides the line segment joining the points A (x_{1}, y_{1}) and B(x_{2}, y_{2}), internally, in the ratio m_{1}: m_{2} is given by the section formula: P(x, y) = [(mx_{2} + nx_{1 }/ m + n)] , [(my_{2} + ny_{1 }/ m + n)]

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

Since the diagonals of a parallelogram bisect each other, intersection point O of diagonal AC and BD also divides these diagonals in the ratio 1:1

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, so, (x + 1) / 2 = 7 / 2 and 4 = (5 + y) / 2

⇒ x + 1 = 7 and 5 + y = 8 (By cross multiplying & transposing)

⇒ x = 6 and y = 3

**Video Solution:**

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

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.2 Question 6:

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

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