Question

The point $A(2,1)$ is translated parallel to the line $x-y=3$ by a distance $4$ units. If the new position $A^{\prime }$ is in third quadrant, then the coordinates of $A^{\prime }$ are:

• A. $(2+2\sqrt{2},2+2\sqrt{2})$
• B. $(-2+\sqrt{2},-1-2\sqrt{2})$
• C. $(2-2\sqrt{2},1-2\sqrt{2})$
• D. $(-2-\sqrt{2},-1-2\sqrt{2})$

Answer 1

Answer: (C)

$(2-2\sqrt{2},1-2\sqrt{2})$

$y=x-3$ $\Rightarrow m=1$ ; $tan\theta =1$
By parametrization we have $x=2\pm rcos\theta$
$y=1\pm rsin\theta$

$x=2\pm 4\times \frac{1}{\sqrt{2}};y=1\pm 4\times \frac{1}{\sqrt{2}}$.....(consider -ive sign for third quadrant)
$x=2-2\sqrt{2};y=1-2\sqrt{2}$ since they are in third quadrant.