Question

Statement-1: Only one straight line can be drawn passing through the origin, at equal distances from the points A(2, 2) and B(4, 0). Statement-2: Only one straight line can be drawn passing through two given points.

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false
• D. Statement-1 is false, statement-2 is true

Answer 1

Answer: (D)

Let $y=m x$
$\therefore \left|\frac{2 m-2}{\sqrt{1+m^2}}\right|=\left|\frac{4 m}{\sqrt{1+m^2}}\right| $
$\therefore 2 m-2= \pm 4 m $
$\therefore m=-1 \text { or } m=1 / 3$
$\text { Also slope of } A B=-1$
Hence there can be two lines $l_1$ and $l_2$ through origin with slopes $1 / 3$ and -1 which are equidistant from $(2,2)$ and $(4,0)$