Question

From (1,4) you travel $5\sqrt{2}$ units by making ${135}^0$ angles with positive x-axis (anticlockwise) and then 4 units by making ${120}^0$ 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: (A)

$(+6,9-2\sqrt{3})$

Let the initial coordinates be $P(x_0,y_0)=P(1,4)$

Let the unknown points be $R(x_1,y_1)$ and $Q(x_2,y_2)$

$x_1=x_0+5\sqrt{2}cos\left({135}^{\circ }\right)$

$\Rightarrow x_1=1+5\sqrt{2}\times (-\frac{1}{\sqrt{2}})=-4$

and, $y_1=y_0+5\sqrt{2}sin\left({135}^{\circ }\right)$

$y_1=4+5\sqrt{2}\times \frac{1}{\sqrt{2}}=9$

Similarly, $x_2=x_1+4cos(-{120}^{\circ })$

$\Rightarrow x_2=-4+4\times (-\frac{1}{2})=-6$

and, $y_2=y_1+4sin(-{120}^{\circ })$

$\Rightarrow y_2=9-4\times \frac{\sqrt{3}}{2}=9-2\sqrt{3}$

Coordinates of $Q(-6,9-2\sqrt{3})$