Question

Plot the segment PQ with endpoints P(-1,-2) and Q(3,3) on the coordinate plane. Then find the length

Answer 1

Check the picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3-(-1)]^2+[3-(-2)]^2}\implies PQ=\sqrt{(3+1)^2+(3+2)^2} \\\\\\ PQ=\sqrt{4^2+5^2}\implies PQ=\sqrt{16+25}\implies PQ=\sqrt{41}\implies PQ\approx 6.4 \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{3-1}{2}~~,~~\cfrac{3-2}{2} \right)\implies \left( \cfrac{2}{2}~,~\cfrac{1}{2} \right)\implies (1~,~0.5)$