A = ( 0 , 0 ), B = ( 3 , 6 ), C = ( 5 , 5 ) and B = ( 2 , −1 )
AB = √[(3-0)^2 + (6 - 0)^2] = √(9 + 36) = √45
BC = √[(3-5)^2 + (6 - 5)^2] = √(4 + 1) = √5
CD = √[(2-5)^2 + (-1 - 5)^2] = √(9 + 36) = √45
AD = √[(2-0)^2 + (-1 - 0)^2] = √(4 + 1) = √5
AB = CD = √45 and BC = AD = √5 ...So this can't be a square or rhombus because square and rhombus have 4 equal sides. It's a rectangle.
Slope of AB = 6/3 = 2
Slope of BC = (6 - 5) / (3 -5) = -1/2
Both slopes are opposite and reciprocal so both lines are perpendicular(AB ⊥ BC)
Answer is the last option
AB ⊥ BC; therefore, ABCD is a rectangle.
Hope it helps.
