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 find $x_1+y_1$

• A. $\frac{-13}{6}$
• B. $\frac{3}{2}$
• C. $\frac{-33}{6}$
• D. $\frac{-23}{6}$

Answer 1

The correct option is D $\frac{-23}{6}$

First we need to find the equation of the line joining the points $(2,-1)$ and $(5,-3)$
Using two point form :
$y+1=\frac{-1+3}{2-5}(x-2)$
$y+1=\frac{2}{-3}(x-2)$
-3($y+1)=2(x-2)$
$\Rightarrow 2x+3y-1=0$

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, $(x_1+y_1)$ = $\frac{5}{3}$ +($-\frac{11}{2}$)
$\Rightarrow \frac{10-33}{6}$
$\Rightarrow \frac{-23}{6}$