Question

Find the distance between the two points in simplest radical form (4,6) and (-2,9)

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{(-2-4)^2+(9-6)^2}\implies d = \sqrt{(-6)^2+3^2}\implies d = \sqrt{36+9} \\\\\\ d = \sqrt{45}\implies d = \sqrt{9\cdot 5}\implies d=\sqrt{3^2\cdot 5}\implies d = 3\sqrt{5}$