A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangle. Show your work.

Answer:The quadrilateral is not a rectangleStep-by-step explanation:we know thatIf a quadrilateral ABCD is a rectanglethenOpposite sides are congruent and parallel and adjacent sides are perpendicularRemember thatIf two lines are parallel, then their slopes are the sameIf two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)The formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]we haveA(-5,5), B(1,8), C(4,2), and D(-2,-2)Plot the figure to better understand the problemsee the attached figureFind the slope of the four sides and then comparestep 1Find slope ABA(-5,5), B(1,8)substitute in the formula[tex]m=\frac{8-5}{1+5}[/tex][tex]m=\frac{3}{6}[/tex][tex]m_A_B=\frac{1}{2}[/tex]step 2Find slope BCB(1,8), C(4,2)substitute in the formula[tex]m=\frac{2-8}{4-1}[/tex][tex]m=\frac{-6}{3}[/tex][tex]m_B_C=-2[/tex]step 3Find slope CDC(4,2), and D(-2,-2)substitute in the formula[tex]m=\frac{-2-2}{-2-4}[/tex][tex]m=\frac{-4}{-6}[/tex][tex]m_C_D=\frac{2}{3}[/tex]step 4Find slope ADA(-5,5), D(-2,-2)substitute in the formula[tex]m=\frac{-2-5}{-2+5}[/tex][tex]m=\frac{-7}{3}[/tex][tex]m_A_D=-\frac{7}{3}[/tex]step 5Verify if the opposites are parallelRemember thatIf two lines are parallel, then their slopes are the sameThe opposite sides are AB and CDBC and ADwe have[tex]m_A_B=\frac{1}{2}[/tex][tex]m_C_D=\frac{2}{3}[/tex]so[tex]m_A_B \neq m_C_D[/tex]It is not necessary to continue verifying, because two of the opposite sides are not parallelthereforeThe quadrilateral is not a rectangle