Question

Find the distance between (0, 2 sqrt 5) and (-2 sqrt 6 , 0)

Answer 1

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{2√(5)})\qquad (\stackrel{x_2}{-2√(6)}~,~\stackrel{y_2}{0})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=\sqrt{(-2√(6)-0)^2+(0-2√(5))^2}\implies d=\sqrt{(-2√(6))^2+(-2√(5))^2} \\\\\\ d=\sqrt{(2^2\cdot (√(6))^2)+(2^2\cdot (√(5))^2)}\implies d=√((4\cdot 6)+(4\cdot 5)) \\\\\\ d=√(24+20)\implies d=√(44)\implies d=√(2^2\cdot 11)\implies d=2√(11)`