Question

Only 9 and 10 please, thank you!! Right answers only with explanation :)

Answer 1

Check the picture below.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{1}~,~\stackrel{y_2}{4})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AB=√([1-(-4)]^2+[4-2]^2)\implies AB=√((1+4)^2+(4-2)^2) \\\\\\ AB=√(5^2+2^2)\implies AB=√(25+4)\implies \boxed{AB=√(29)} \\\\[-0.35em] ~\dotfill`

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_2}{1}~,~\stackrel{y_2}{4})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1})~\hfill BC=√((2-1)^2+(-1-4)^2) \\\\\\ BC=√(1^2+(-5)^2)\implies BC=√(1+25)\implies \boxed{BC=√(26)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill √(29)~~\\e~~√(26)~\hfill`