Question

The points $(-1,1)$ and $(1,-1)$ are symmetrical about the line

• A. $y+x=0$
• B. $y=x$
• C. $x+y=1$
• D. None of these

Answer 1

The correct option is B $y=x$

The pts are symmetrical abt. line if the $\perp$ distance from the

line is equal

Then mid pt of A(-1,1) and B(1,-1) is

$(\frac{-1+1}{2},\frac{1-1}{2})=(0,0)$ [using section formula]

(m) slope of line $\perp$ to AB = $\frac{-1}{m_{AB}}$

$m_{AB}=\frac{-1-1}{1+1}=-1$

$m=1$

$\Rightarrow e{q}^n$ of line is y=x $[\because$ using $y-y_1=m(x-x_1)]$

$\Rightarrow$ pts are symmetrical about y=x