Point `P(2, 4)` is translated through a distance `3sqrt2` units measured parallel to the line `y-x-1 = 0` in the directionof decreasing ordinates to reach at Q. If R is the imageof Q with respect to the line `y-x-1 = 0`, then thecoordinates of R are given by (1) `(5,7)` (2) `(-1,1)` (3) `(6,6)` (4) `(0,0)`

Options

A. (-1,1)
B. (5,7)
C. (6,6)
D. (0,0)

Explanation

The equation of a line through P( 2, 4) and parallel to y - x - 1 = 0 is
`(x -2)/(cos pi //4) = (y-4)/(sin pi//4)`
The coordinates of Q are given by
gt `(x -2)/(cos pi //4) = (y-4)/(sin pi//4) = -3sqrt2 implies x = -1 , y = 1`
Thus , the coordinates of Q are (-1,1).
R is the image of Q with respect to the line y - x - 1 = 0 .
Therefore , coordinate of R is given by
`( x + 1)/(-1) = (y-1)/(1) = -2 ((1 + 1+ -1))/((-1)^(2) + (1)^(2))`
`implies (x + 1)/(-1) = (y-1)/(1) = -1 implies x = 0 , y = 0 `
Hence , the coordinates of R are (0,0) .