Question

From $(1,4)$ you travel $5 \sqrt{2}$ units by making $135^{\circ}$ angle with positive $x$-axis (anticlockwise) and then $4$ units by making $120^{\circ}$ angle with positive $x$-axis (clockwise) to reach $Q$. Find co-ordinates of point $Q$.

• A. $(+6,9-2 \sqrt{3})$
• B. $(-6,9-2 \sqrt{3})$
• C. $(-6,9+2 \sqrt{3})$
• D. $(+6,9+2 \sqrt{3})$

Answer 1

Answer: (B)

For point $P \frac{x-1}{\cos 135^{\circ}}=\frac{y-4}{\sin 135^{\circ}}=5 \sqrt{2} $
$\Rightarrow x=-4, y=9$
For point $Q$
$\frac{x+4}{\cos \left(-120^{\circ}\right)}=\frac{y-9}{\sin \left(-120^{\circ}\right)}=4 $
$\Rightarrow x=-6, y=9-2 \sqrt{3}$
$\therefore Q(-6,9-2 \sqrt{3})$.