Question

The equation of the line passing through the point of intersection of the lines $2x+y=5$ and $y=3x-5$, and which is at the minimum distance from the point $(1,2)$ is

• A. $x+y=3$
• B. $x-y=1$
• C. $x-2y=0$
• D. $2x+5y=7$

Answer 1

Answer: (A)

$x+y=3$

$2x+y=5\to \left(1\right)$
$3x-y=5\to \left(2\right)$
from 1 & 2,
$x=2,y=1$
The line at a minimum distance from $(1,2)$ and passing through $(2,1)$ will be the line passing through the two points.
$\therefore$ equation of line is
$y-1=\left(\frac{1-2}{2-1}\right)(x-2)$
$y+x=3$