Answer:
ABCD is a rectangle
Step-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
