Question

Find the point of intersection of the line that passes through the points $(1,5)$ and $(3,9)$ and the line perpendicular to that line that passes through the point $(0,-2)$.

• A. $(-2,-1)$
• B. $(-2,2)$
• C. $(2,-2)$
• D. $(-1,-2)$
• E. $(1,2)$

Answer 1

The correct option is A $(-2,-1)$

Equation of the line passing through $(1,5)$ and $(3,9)$ is

$(y-5)=\frac{9-5}{3-1}(x-1)$

$\Rightarrow y-5=2x-2$

$\Rightarrow 2x-y+3=0$

Slope of $2x-y+3=0$ is $\frac{-2}{-1}=2$

Slope of the line perpendicular to $2x-y+3=0$ is $-\frac{1}{m}=-\frac{1}{2}$

Line passing through $(0,-2)$ and perpendicular to $2x-y+3=0$ is

$(y-(-2\left)\right)=-\frac{1}{2}(x-0)$

$\Rightarrow 2(y+2)+1\left(x\right)=0$

$\Rightarrow x+2y+4=0$

Point of intersection of $x+2y+4=0$ and $2x-y+3=0$ is $(-2,-1)$