Question

The point (2, 1) is shifted through a distance 3√2 units measured parallel to the line x + y = 1 in the decreasing direction of ordinates to reach a point B. The image of the point Bin the line x + y = 1 is

(A)  (0, 0)

(B)  (0, -1)

(C)  (-3,2)

(D)  (3,-4)

Answer 1

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.