Question

An isosceles trapezoid has vertices at (-2, 1), (2, 1), (5, -1) and (-5, -1). find the measure of each diagonal

Answer 1

Check the picture below.

well, is an isosceles trapezoid, namely the slanted sides are equal, so the diagonals, in red, are also equal, so let's just find the length of the solid line diagona, since the dashed one will be the same length anyway.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([2 - (-5)]^2 + [1 - (-1)]^2)\implies d=√((2+5)^2+(1+1)^2) \\\\\\ d=√(7^2+2^2)\implies d=√(53)\implies d\approx 7.28`