The point A(2,1) is translated parallel to the linen x-y=3 by a distance of 4 units. If the new position A' is in the third quadrant, then the coordinates of A' are

Options

A. `(2+2sqrt(2),1+2sqrt(2))`
B. `(-2+sqrt(2),-1-2sqrt(2))`
C. `(2-2sqrt(2),1-2sqrt(2))`
D. none of these

Answer

C

Explanation

Since the point A(2,1) is translated parallel to `x-y=3`. Therefore, AA' has the same slope as that of x-y=3 . Thus, AA' passes through (2,1) and has the slope =1.
So, the equation of AA' is
`(x-2)/(cos pi//4)=(y-1)/(sin pi//4)`

Since, AA'=4 . Therefore , coordinates of A' are given by
`(x-2)/(cospi//4)=(y-1)/(sin pi//4)=-4`
`implies x=2-4"cos"(pi)/(4), y=1-4"sin" (pi)/(4)`
`impliesx=2-2sqrt(2),y=1-2sqrt(2)`.
Hence , the coordinates of A' are `(2-2sqrt(2),1-2sqrt(2))`