Answer:
Option C
Explanation:
As the given lines x-y+1=0 and 7x-y-5=0 are not parallel, therefore they represent the adjacent sides of the rhombus
On solving x-y+1=0 and 7x+y-5=0 , we get x=1 and y=2, thus, one of the vertex is A(1,2)
Let the coordinates of point C be (x,y)
Then, $-1=\frac{x+1}{2}$ and $-2=\frac{y+2}{2}$
$\Rightarrow x+1=-2 $ and $y=-4-2$
$\Rightarrow x=-3$ and $y=-6$
Hence, coordinates of C =(-3,-6)
Note that vertices B and D will satisfy x-y+1=0 and 7x-y-5=0
respectively
Since option(c) satisfies 7x-y-5=0, therefore coordinates of vertex D is $(\frac{1}{3},-\frac{8}{3})$
