Question

A is the point (10,4) and B is the point (4,-6).

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{4+10}{2}~,~\cfrac{-6+4}{2} \right)\implies (7,-1) \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{origin}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad \stackrel{\textit{midpoint of AB}}{(\stackrel{x_2}{7}~,~\stackrel{y_2}{-1})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(7-0)^2+(-1-0)^2}\implies d=\sqrt{7^2+(-1)^2} \\\\\\ d=\sqrt{48}\implies d\approx 6.93$