that's just the distance between 2 points
the distance between (x1,y1) and (x2,y2) is
[tex]D= \sqrt{(x2-x1)^2+(y2-y1)^2} [/tex]
we can find the distance between S and Q or P and R
S and Q is (0,0) and (a,b)
[tex]D= \sqrt{(a-0)^2+(b-0)^2} [/tex]
[tex]D= \sqrt{a^2+b^2} [/tex]
distance between P and R is between(0,b) and (a,0)
[tex]D= \sqrt{(a-0)^2+(0-b)^2} [/tex]
[tex]D= \sqrt{(a)^2+(-b)^2} [/tex]
[tex]D= \sqrt{a^2+b^2} [/tex]
[tex] \sqrt{a^2+b^2} = \sqrt{a^2+b^2} [/tex]
so the lengths of diagonals are congruent
