Question

Use the Distance Formula and the Pythagorean Theorem to find the distance between each pair of points. M (5, −3) and N (4, −8)

Answer 1

well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ MN=√([4-5]^2+[-8-(-3)]^2)\implies MN=√((4-5)^2+(-8+3)^2) \\\\\\ MN=√((-1)^2+(-5)^2)\implies MN=√(26)`