Question

Two sides of a parallelogram are along the lines x+y = 3 and x-y = -3 . If it's diagonals intersects at (2,4) then one of its vertex is Options 1.(2,6) 2.(3,6) 3.(2,5) 4.(3,5)

Answer 1

Answer: The answer is (4,5).

Step-by-step explanation:   As given in the question and shown in the attached figure, ABCD is a parallelogram where

the equation of side AB is

$x+y=3,$

and equation of side BC is

$x-y=-3.$

Also, the diagonals AC and BD intersect each other at the point O(2,4).

Now, solving the equations for sides AB and BC, we get

$x=0~~\textup{and}~~y=3.$

Therefore, co-ordinate of the vertex B are (0,3). We are to find the co-ordinates of the vertex D.

Since the diagonals of a parallelogram bisect each other, so 'O' will be the mid-point of BD.

Let (a,b) be the co-ordinates of the vertex B, then

$\left(\dfrac{0+a}{2},\dfrac{3+b}{2}\right)=(2,4)\\\\\\\Rightarrow a=4,~~b=5.$

Thus, the co-ordinates of the other vertex are (4,5).

Answer 2

Answer:(౩,6)

Step-by-step explanation:check this image out