Question

find the perpendicular distance between (2,5) and the line 2x - y + 7 = 0 in a surd form with a rational denominator

Answer 1

`The\ distance\ between\ P(x_P;\ y_P)\ and\ the\ line\ Ax+By+C=0:\\\\d=(|Ax_P+By_P+C|)/(√(A^2+B^2))\\===================================\\P(2;\ 5);\ 2x-y+7=0\\\\x_P=2;\ y_P=5;\ A=2;\ B=-1;\ C=7\\\\d=(|2*2-1*5+7|)/(√(2^2+(-1)^2))=(|4-5+7|)/(√(4+1))=(|6|)/(\sqrt5)\cdot(\sqrt5)/(\sqrt5)=(6\sqrt5)/(5)`