Point P (2, 4) is translated through a distance32 units measured parallel to the line y - x -1 = 0, in the direction of decreasing ordinates, to reach at Q. If R is the image ofQ unth respect to the line y - x -1 = 0, then coordinates of R are

The equation of a line through P (2, 4) and parallel to y - x - 1 = 0 isx−2cos⁡π/4=y−4sin⁡π/4The coordinates of Q are given byx−2cos⁡π/4=y−4sin⁡π/4=−32⇒x=−1,y=1Thus, the coordinates of Q are (-1, 1). R s the image of Q with respect to the line y - x -1 = 0.Therefore, coordinates of R are given byx+1−1=y−11=−2(1+1−1)(−1)2+(1)2x+1−1=y−11=−1⇒x=0,y=0Hence, the coordinates of R are (0, 0).