If one diagonal of square is the portion of the line `x/a+y/b=1`intercepted by the axes, then the extremities of the other diagonal of the square are :

Options

A. (5,5), (-1,1)
B. (0,0), (4,6)
C. (0,0),(-1,1)
D. (5,5),(4,6)

Answer

A

Explanation

The extremities of the given diagonal are (4,0) and (0,6) Hence, the slope of this diagonal is -3/2 and the slope of other diagonal is 2/3. The equation of the other diagonal is
`(x-2)/(3//sqrt(13)) = (y-3)/(2//sqrt(13)) =r`
For the extremities of the diagonal, `r =+-sqrt(13).` Hence,
`x-2 = +-3, y-3=+-2`
x=5,-1 and y5,1
Therefore, the extremities of the diagonal are (5,5) and (-1,1).