Question

Prove that the points (−7, −3), (5, 10), (15, 8) and (3, −5) taken in order are the corners and find its area

Answer 1

let A=(-7,-3)
     B=(5,10)
     C=(15,8)
     D=(3,-5)
dist.b/w AB = ([-7-5]^2 + [-3-10]^2) ^1/2
                   = (144 + 169)^1/2
                   = (313)^1/2 = 17.69
dist.b/w BC = ([5-15]^2 + [10-8]^2)^1/2
                   = (100 + 4)^1/2
                   = (104)^1/2 = 10.19
dist.b/w CD = ([15-3]^2[8+5]^2)^1/2
                   = (144 + 169)^1/2
                   =(313)^1/2 = 17.69
dist.b/w AD = ([-7-3]^2[-3+5]^2)^1/2
                   = (100 + 4 )^1/2
                   = (104)^1/2 = 10.19
=> 
     opp. sides are equal in the fig.
  area = l * b
          = 17.69*10.16
          = 180.26 sq.units