Question

A line passes through the point (2, 3) and perpendicular to the line joining (-5, 6) and (-6, 5) is given by :

• A. x + y + 5 = 0
• B. x + y - 5 = 0
• C. x - y - 5 = 0
• D. x - y + 5 = 0

Answer 1

The correct option is B x + y - 5 = 0

The equation of any straight line can be written as $y=mx+c$, where $m$
is its slope and $c$ is its y - intercept.
Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ $=$ $\frac{y_2-y_1}{x_2-x_1}$

So, slope of the line joining $(-5,6),(-6,5)=\frac{-6+5}{5-6}=1$

Slope of the line perpendicular to this line $=-1$

So, equation of the required line will be $y=-x+c$

Since, this line passes through $(2,3)$, on substituting $(2,3)$ in the equation we get

$3=-2+c$

$=>c=5$

Hence, required equation of the line is $y=-x+5$ or $x+y-5=0$