Triangle ABC
A(4,-2)
B(5,5)
C(-1,3)
To calculate each side length you have to apply the Pythagoras theorem:
Considering each side of the triangle as the hypothenuse of a rigth triangle you can say that their base and heigth will be determined by their coordinates over the x and y axis so that:
Then:
Finally:
Side AB
c=AB
A(4,-2) B(5,5)
Side BC
c=BC
B(5,5) C(-1,3)
Side AC
c= AC
A(4,-2) C(-1,3)
Acording to the calculated lengths AB≅AC
The correct option is a)