Question

The coordinates of the vertices a(7,2) b(9,10) c(1,4). If e and f are the midpoint of ab and ac respectively prove that ef is equal to half of bc​

Answer 1

Answer:

Step-by-step explanation:

midpoint of ab e(x,y) = 1/2 (7+9) + 1/2 (10+2)

                                    = (8,6)

midpoint of ac f(x,y) = 1/2(7+1) + 1/2 (2+4)

                                  = (4,3)

ef = √(x₂-x₁)²+ (y₂-y₁)2

   = √(8-4)² + (6-3)²

        =√25

       =5cm

bc=√ (x₂-x₁)² -(y₂-y₁)²

     = √(9-1)² + (10-4)²

      =√64 +36

      =√100

        = 10

ef=1/2 x bc

5  = 1/2 x 10

5 = 5

hence proved