Question

One diagonal of a square is the portion of the line $7x+5y=35$ intercepted by the axes, then the extremities of the other diagonal are :-

• A. $(6,6)$
• B. $(5,7)$
• C. $(-1,1)$
• D. $(7,5)$

Answer 1

Answer: (A), (C)

The correct options are
A $(6,6)$
C $(-1,1)$

Mid point of one diagonal is $(\frac{5}{2},\frac{7}{2})$
Also lenght of the diagonal $=\sqrt{25+49}=\sqrt{74}$
Slope of line perpendicular to that diagonal $=\frac{5}{7}$
Equation of other diagonal which is perpendicular to the idagonal and passing through the point is
$\frac{x-5/2}{7/\sqrt{74}}=\frac{y-7/2}{5/\sqrt{74}}=r$

Substitute $r=\pm \frac{\sqrt{74}}{2}$, coordinate of the extremities are $(6,6)$ and $(-1,1)$