The point (2, 1) is translated parallel to the line L: x - y = 4 by...

Equation of line $QR$ perpendicular to $L: x - y = 4$ is
$x + y - c = 0 \ldots \left(1\right)$

Distance of $QR$ from \left(2, 1\right)$is$2\sqrt{3}$<br /><br />$⇒ 2\sqrt{3} = \dfrac{\left|2 + 1 - c\right|}{\sqrt{2}}$<br /><br />$⇒ 2\sqrt{6} = \left|3 - c\right|$<br /><br />$⇒ c - 3 = \pm 2\sqrt{6} ⇒ c = 3 \pm 2\sqrt{6}$<br /><br />Line can be$x + y = 3 \pm 2\sqrt{6}$<br /><br />$x + y = 3 - 2\sqrt{6}$(since$Q is in the third quadrant)