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What is the area of a rectangle with vertices at (-6, 3), (-3, 6). (1, 2), and (-2, -1)?
Enter your answer in the hoy nn nnt round ans side lennths​

Answer 1

Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d = √([-3-(-6)]^2+[6-3]^2)\implies d=√((-3+6)^2+(6-3)^2) \\\\\\ d=√(9+9)\implies \boxed{d=√(18)} \\\\[-0.35em] ~\dotfill`

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=√([-2-(-6)]^2+[-1-3]^2) \\\\\\ d=√((-2+6)^2+(-1-3)^2)\implies d=√(16+16)\implies \boxed{d=√(32)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(√(18))(√(32))}\implies √(18\cdot 32)\implies √(576)\implies 24`