The correct option is B (−1,0)
Assuming the vertices be
A(x1,y1)=(−36,7)
B(x2,y2)=(20,7)
C(x3,y3)=(0,−8)
Now, the side lengths are
a=BC=25 units
b=AC=39 units
c=AB=56 units
Now, the incentre
∴I=(ax1+bx2+cx3a+b+c,ay1+by2+cy3a+b+c)
⇒I=(25(−36)+39(20)+56(0)25+39+56,25(7)+39(7)+(−8)5625+39+56)⇒I=(−25(36)+39(20)120,64(7)−56(8)120)⇒I=(20(−45+39)6,64(7−7)120)
∴I=(−1,0)