Show that the points (1,-2), (3,0), (1,2) and (-I,0) are the vertices of square a

Question

Show that the points (1,-2), (3,0), (1,2) and (-1,0) are the vertices of a square.

Answer 1

Let P(1,-2), Q(3,0), R(1,2) and S(-1,0) be the given points

Then,

 

and diagonal QS= 

Since  PQ=QR=RS=SP= √8  all sides equal, 

diagonal PR = diagonal QS = 4,

diagonals are equal

Hence PQRS is a square.