Question

One of the diagonals of a square is the portion of the line $x/2+y/3=2$ intercepted between the axes. Then the extremities of the other diagonal are

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

Answer 1

Answer: (A)

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 $\frac{x-2}{3/\sqrt{13}}=\frac{y-3}{2/\sqrt{13}}=r$
For the extremities of the diagonal, $r=\pm \sqrt{13}$. Hence,
$x-2=\pm 3,y-3=\pm 2$
$x=5,-1\text{ and }y=5,1$
Therefore, the extremities of the diagonal are $(5,5)$ and $(-1,1)$.