In the coordinate plane, draw quadrilateral ABCD with A(–5, 0), B(2, –6), C(8, 1), and D(1, 7), then demonstrate that ABCD is a rectangle.

Answer:ABCD is a rectangleStep-by-step explanation:∵ A = (-5 , 0) , B = (2 , -6) , C = (8 , 1) , D = (1 , 7)∵ The x-coordinate of the mid-point of AC = (-5 + 8)/2 =3/2∵ The y-coordinate of the mid-point of AC = (0 + 1)/2 = 1/2∴ The mid-point of AC = (3/2 , 1/2)∵ The x-coordinate of the mid-point of BD = (2 + 1)/2 =3/2∵ The y-coordinate of the mid-point of BD = (-6 + 7)/2 = 1/2∴ The mid-point of BD = (3/2 , 1/2)∴ The mid-point of AC = The mid-point of BD ⇒ (1)∵ AC = √[(8 - -5)²+(1 - 0)² = √170∵ BD = √[(1 - 2)²+(7 - -6)² = √170∴ AC = BD ⇒ (2)From (1) and (2)AC and BD equal each other and bisects each other∴ ABCD is a rectangle