Question

Derive the formula for distance of a points $(x_1,y_1)$ from a line $Ax+By+C=0$ and find the distance of the points. $(3,-5)$ from the line $3x-4y-26=0$

Answer 1

Formula for distance of a point $(x_1,y_1)$ from a line $Ax+By+C=0$ is $\frac{|A{x}_1+B{y}_1+C|}{\sqrt{A^2+B^2}}$

$\therefore$the distance of a point $(3,-5)$ from a line $3x-4y-26=0$ is $\frac{|3\left(3\right)-4(-5)-26|}{\sqrt{9+16}}$

$\therefore$distance =$\frac{3}{5}$