Question

Justify that a (4,3) , b ( 6, 4) , c ( 5, - 6) , and d ( - 3 , 5) are the vertices of a parallelogram.

Answer 1

using distance formula,

AB² = (4-6)² + (3-4)² = 4+1 =5

CD² = (3-5)² + (-7+6) = 4+1 =5

CD² = (4-3)² + (3-7)² = 1+100 = 101

BC² = (6-5)² + (4-6)² = 1+100 = 101

As, AB² = CD² = 5

     CD² = BC² = 101

Opposie sides are equal,so ABCD is a parallelogram.