Question

If a point $P(4,3)$ is shifted by a distances $\sqrt{2}$ units parallel to the line $y=x$, then the coordinates of $P$ in its new position are

• A. $(5,4)$
• B. $(5+\sqrt{2},4+\sqrt{2})$
• C. $(5-\sqrt{2},4-\sqrt{2})$
• D. $(4,5)$

Answer 1

The correct option is A $(5,4)$

shifted by $\sqrt{2}$ units $\Rightarrow r=\sqrt{2}$
for the line is tan $\theta =1$
$\therefore$ by parametric equations, we have
$x=x^1+rcos\theta$ ; $y=y^1+rsin\theta$
$\Rightarrow x=4+\sqrt{2}\frac{1}{\sqrt{2}}$ ; $y=3+\sqrt{2}\frac{1}{\sqrt{2}}$
$x=5$ ; $y=4$