Question

The graphs of x + 2y = 3 and 3x - 2y = 1 meet the y-axis at two points having distance between them of?

• A. $\frac{8}{3}$ units
• B. $\frac{4}{3}$ units
• C. $1$ units
• D. $2$ units
• E. None of the above

Answer 1

The correct option is D $2$ units

On y-axis, x = 0
Putting x = 0 in x + 2y = 3,
$2y=3\Rightarrow y=\frac{3}{2}$
Putting x = 0 in 3x - 2y = 1
$-2y=1\Rightarrow y=-\frac{1}{2}$
$\therefore$ Points on y - axis are $(0,\frac{3}{2})$ and $(0,-\frac{1}{2})$
$\therefore$ Required distance $=\sqrt{(0-0{)}^2+{(\frac{3}{2}+\frac{1}{2})}^2}$
$=\sqrt{0+4}=2units$