Question

Find the distance from P to l.

Line l contains points (-4,2) and (3,-5).
Point P has coordinates (1,2).

Answer 1

`Equation\ of\ a\ line\ from\ 2\ points (x_1;\ y_1);\ (x_2;\ y_2):\\\\y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\(-4;\ 2)\ and\ (3;-5)\\subtitute:\\\\y-2=(-5-2)/(3-(-4))\cdot(x-(-4))\\\\y-2=(-7)/(7)\cdot(x+4)\\\\y-2=-(x+4)\\\\y-2=-x-4\ \ \ |add\ x\ and\ 4\ to\ both\ sides\\\\x+y+2=0\\-------------------\\`


`Point-line\ distance\\l:Ax+By+C=0;\ (x_0;\ y_0)\\\\d=(|Ax_0+By_0+C|)/(√(A^2+B^2))\\\\x+y+2=0\to A=1;\ B=1;\ C=2\\(1;\ 2)\to x_0=1;\ y_0=2\\subtitute\\\\d=(|1\cdot1+1\cdot2+2|)/(√(1^2+1^2))=(|1+2+2|)/(\sqrt2)=(|5|)/(\sqrt2)=(5)/(\sqrt2)=(5\cdot\sqrt2)/(\sqrt2\cdot\sqrt2)\\\\=\boxed{(5\sqrt2)/(2)}`