Question

Given A(-2,1) and B(3,-4)

1) find the distance between A and B
2) Find the midpoint of segment A and B

Answer 1

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`\bf -------------------------------\\\\ ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})\qquad \qquad % distance value d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AB=√([3-(-2)]^2+[-4-1]^2)\implies AB=√((3+2)^2+(-4-1)^2) \\\\\\ AB=√(25+25)\implies AB=√(2\cdot 25) \\\\\\ AB=√(2\cdot 5^2)\implies AB=5√(2)\\\\ -------------------------------\\\\`

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})\qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{3-2}{2}~~,~~\cfrac{-4+1}{2} \right)\implies \left((1)/(2)~~,~~-(3)/(2) \right)\implies \left((1)/(2)~~,~~-1(1)/(2) \right)`