Question

Show that the points A(6, 2), B(2, 1), C(1, 5) and D(5, 6) are the vertices of a square. OrFind the co-ordinates of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5). ...................... :) ;)

Answer 1

we look A (6,2) ,B (2,1) ,C (1,5) andD (5,6)
now
first of all find distance AB, BC, and AC
and apply pythagorus theorem
so, AB=root {(6-2)^2+(2-1)^2}=root(17)
BC=root {(2-1)^2+(1-5)^2}=root (17)
AC=root {(6-1)^2+(2-5)^2}=root(34)
now above we see that
AB=BC
apply Pythagoras theorem
AB^2+BC^2=AC^2
hence
all conditions fulfilled to square by A, B, C and D point so ABCD is square