If A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram taken in order, - Maths - Coordinate Geometry

Question

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

i hv found AD = sqroot 13 bt i m not getting how to
proceed further

Lalit Mehra · Accepted Answer

Dear Student!

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

We know that, the diagonals of the parallelogram bisect each other.

∴ Mid Point if diagonal $BD = (\frac{4 + 3}{2}, \frac{y + 5}{2}) = (\frac{7}{2}, \frac{y + 5}{2})$

Mid point of diagonal $AC = (\frac{1 + x}{2}, \frac{2 + 6}{2}) = (\frac{1 + x}{2}, 4)$

Now, Mid point of diagonal BD = Mid Point of diagonal AC

∴ $(\frac{7}{2}, \frac{y + 5}{2}) = (\frac{1 + x}{2}, 4)$

$\Rightarrow \frac{1 + x}{2} = \frac{7}{2} and \frac{y + 5}{2} = 4$

⇒ 1+ x = 7 and y + 5 = 8

⇒ x = 7 – 1 and y = 8 – 5

⇒ x = 6 and y = 3

Thus, the value of x and y is 6 and 3 respectively.

Cheers!

If A(1, 2), B(4, y ), C( x , 6) and D(3, 5) are the vertices of a parallelogram taken in order, find x and y . i hv found AD = sqroot 13 bt i m not getting how to proceed further