Question

Ir (1, 2), (4,y),(x, 6) and (3, 5) are the vertices of
a parallelogram taken in order, find x and y.
Answer karo na yaar....​

Answer 1

Answer:

we know in parallelogram, diagonals bisect each other.

so midpoint of diagonal AC = midpoint of diagonal BD.

Using midpoint formula

[(1+x)/2, (2+6)/2] = [(4+3)/2, (y+5)/2]

so on comparing

1+x = 7

x = 6

8 = y + 5

y = 3

Answer 2

                        Answer

We know, the opposite sides of parallelogram are equal.

Using distance formula,

$\sqrt{(4-1)^{2}+(y-2)^{2} } = \sqrt{(3-x)^{2}+(5-6)^{2} }$

$\sqrt{3^{2}+(y-2)^{2} }=\sqrt{(3-x)^{2}+(1)^{2} }$

$\sqrt{9+(y-2)^{2} }=\sqrt{(3-x)^{2}+1} }$

$(y-2)^{2}=(3-x)^{2} -8$------------------------------------------(1)

Similarly,for the other two sides,

$\sqrt{(4-x)^{2}+(y-6)^{2} } = \sqrt{(3-1)^{2}+(5-2)^{2} }$

$\sqrt{(4-1)^{2}+(y-2)^{2} } = \sqrt{13}$

$(4-1)^{2}+(y-2)^{2} =13$

Two equations,two variable,solve it to get the answer.