The point  A (2, l) is translated parallel to the line x - y = 3 by a distance of 4 units. If the new position A1 is in the third quadrant, then the coordinates of A1 are

Since the point A(2, 1) is translated parallel to x - y = 3, AA' has the same slope as that of x - y = 3. Therefore, AA' passes through (2, 1)  and has slope 1. Here, tan⁡θ=1 or cos⁡θ=1/2,sin⁡θ=1/2Thus, the equation of AA' is x−2cos⁡(π/4)=y−1sin⁡(π/4)Since AA' = 4, the coordinates of A' are given by x−2cos⁡(π/4)=y−1sin⁡(π/4)=−4 or x=2−4cos⁡π4,y=1−4sin⁡π4 or  x=2−22,y=1−22 Hence, the coordinates of A′ are (2−22,1−22) .