Question

A particle is moving in a straight line and at some moment it occupied the positions $(5,2)$ and $(-1,-2)$. Then the position of the particle when it is on $x-$axis is

• A. $(-2,0)$
• B. $(0,2)$
• C. $(2,0)$
• D. $(4,0)$

Answer 1

The correct option is C $(2,0)$

equation of the line

$(y-2)=\frac{2-(-2)}{5-(-1)}(x-5)$
$(y-2)=\frac{4}{6}(x-5)$
$y-2=\frac{2}{3}(x-5)$
Now for $y=0$, it cuts $x$ axes
$0-2=\frac{2}{3}(x-5)$
$-3=x-5$
$x=5-3=2$
So, point is $(2,0)$