**Correct option (D) (3,-4)**

**Explanation :**

See Fig. Let A = (2, 1). By hypothesis, A is translation along the line

y - 1 = -1(x - 2)

x + y = 3 ....(1)

Therefore abscissa of B is given by the equation

(2 - x)^{2} + (2 - x)^{2} = 18

2 - x = *±3*

*x = -1,5*

Hence, the point B = (-1, 4) or (5, -2). However, A(2, 1) is translated in the decreasing sense of ordinates. Thus, B = (5, 2). Hence, the image of B = (5, -2) in the line x + 5 = 1 is B'(3, -4) because the slope of BB' is 1 and the midpoint of BB' is (4, 3) which lies on the line x + y = 0.