Question

If each of the points $(x_1,4),(-2,y_1)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $P(x_1,y_1)$ lies on the line

• A. $6(x+y)-25=0$
• B. $2x+6y+1=0$
• C. $2x+3y-6=0$
• D. $6(x+y)+25=0$

Answer 1

The correct option is B $2x+6y+1=0$

The equation of the line joining the points $(2,-1)$ and $(5,-3)$ is given by
$y+1=\frac{-1+3}{2-5}(x-2)$
$\Rightarrow 2x+3y-1=\mathrm{0....}\left(i\right)$
Since $(x_1,4)$ and $(-2,y_1)$ lie on the line $2x+3y-1=0$, therefore
$2x_1+12-1=0\Rightarrow x_1=-\frac{11}{2}$
and
$-4+3y_1-1=0\Rightarrow y_1=\frac{5}{3}$
Thus, by checking the options $(x_1,y_1)$ satisfies $2x+6y+1=0$