Comprehension \( \quad \) Consider two points \( A=(1,2) \) and \( B=(3,-1) \). Let \( M \) be a...

Comprehension \( \quad \) Consider two points \( A=(1,2) \) and \( B=(3,-1) \). Let \( M \) be a point on the straight line \( L: x+y=0 \).
If \( M \) be a point on the line \( L=0 \) such that \( |A M-B M| \) is minimum, then the area of \( \triangle A M B \) equals
(a) \( \frac{13}{4} \)
(b) \( \frac{13}{2} \)
(c) \( \frac{13}{6} \)
(d) \( \frac{13}{8} \)