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 $y=mx$
$\therefore \left|\frac{2m-2}{\sqrt{1+m^2}}\right|=\left|\frac{4m}{\sqrt{1+m^2}}\right|$
$\therefore 2m-2=\pm 4m$
$\therefore m=-1\text{ or }m=1/3$
$\text{ Also slope of }AB=-1$
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 $(4,0)$