Question

Find the distance of the point of intersection of the lines $2x+3y=21$ and $3x-4y+11=0$ from the line $8x+6y+5=0$.

Answer 1

The point of intersection of two lines can be calculated by solving the equations.

Solving $2x+3y-21$ and $3x-4y+11=0$, we get the point of intersection as p(3, 5)

Distance of p from $8x+6y+5=0$ is

Here, $a=8,b=\pm 6,c=5,x_1=3,y_1=5$

$\frac{|a{x}_1+b{y}_1+c|}{\sqrt{a^2+b^2}}\Rightarrow \frac{|8\left(3\right)+6\left(5\right)+5|}{\sqrt{64+36}}$

$\Rightarrow \frac{|24+30+5|}{\sqrt{100}}=\frac{|59|}{10}$

$\Rightarrow \frac{59}{10}$