Question

What is the distance between the points G(−5, 4) and H(2, 6)?

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ G(\stackrel{x_1}{-5}~,~\stackrel{y_1}{4})\qquad H(\stackrel{x_2}{2}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ GH=\sqrt{[2-(-5)]^2+[6-4]^2}\implies GH=\sqrt{(2+5)^2+(6-4)^2} \\\\\\ GH=\sqrt{7^2+2^2}\implies GH=\sqrt{49+4}\implies GH=\sqrt{53}\implies GH\approx 7.28$