Question

For the point P(19,10) and Q(26,13), find the distance d(P,Q) and the coordinates of the midpoint

M of the segment PQ.

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ PQ=√((~~26 - 19~~)^2 + (~~13 - 10~~)^2) \implies PQ=√(( 7 )^2 + ( 3 )^2) \\\\\\ PQ=√( 49 + 9 ) \implies PQ=√( 58 )\implies PQ\approx 7.62 \\\\[-0.35em] ~\dotfill`

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 26 +19}{2}~~~ ,~~~ \cfrac{ 13 +10}{2} \right) \implies \left(\cfrac{ 45 }{2}~~~ ,~~~ \cfrac{ 23 }{2} \right)\implies \stackrel{ \textit{\LARGE M} }{\left(22(1)/(2)~~,~~11(1)/(2) \right)}`