Q. The point (4, 1) undergoes the following three successive transformations Reflection about the line $y = x - 1$ Translation through a distance 1 unit along the positive direction of $x$-axis Rotation through an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction Then, the coordinates of the final point are
A) $(4,\ 3)$
B) $\left( \frac{7}{2},\frac{7}{2} \right)$
C) $(0,\ 3\ \sqrt{2})$
D) $(3,\ 4)$
Explanation
(c)
If $(\alpha,\beta)$ be the image of (4, 1) w.r.t.$y = x - 1$, then $(\alpha,\ \beta) = (2,\ 3)$ say point $Q$
[image:10_image43.emf]
After translation through a distance 1 unit along the positive direction of $x$-axis at the point whose coordinate are $R \equiv (3,\ 3)$. After rotation through are angle $\pi/4$ about the origin in the anti-clockwise direction, then $R$ goes to $R''$ such that
$OR = OR^{''} = 3\sqrt{2}$
$\therefore$ The coordinates of the final point are $(0,\ 3\sqrt{2})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.