First we have to find coordinates of D.
It will be D = (-4, -8)
(∵ AB = CD & AD = BC for D = (-4, -8))
Now, we have to find coordinates of E.
\(\because DE \perp CD.\)
Let D = (x, y).
\(\left(\frac {y +8}{x+4}\right) \left(\frac{-1+8}{-3+4}\right) = -1\)
⇒ \(7(y+ 8) = - (x +4)\) ......(1)
Also,
\(DE = CD\)
⇒ \((y + 8)^2 + (x + 4)^2 = (-3 + 4)^2 + (-1 + 8)^2\)
⇒ \((y +8)^2 + 49(y +8)^2 = 1 +49\)
⇒ \((y + 8)^2 = 1\)
⇒ \(y +8 = 1\)
⇒ \(y = -8 + 1 = -7\)
\(\therefore x = -7(y +8)-4\)
\(= -7 (-7 + 8)-4\)
\(= -7 -4 \)
\(= -11\)
\(\therefore E =(-11, -7)\)
\(\therefore AE^2 = (2 +11)^2 + (-3 +7)^2\)
\(= 13 ^2 + 4^2 = 169 + 16 = 185\)