Question

In which direction and by what angle should rectangle $ABCD$ be rotated around the point $(0,0)$ such that image $EFGH$ is obtained?

• A. Counterclockwise, ${45}^o$
• B. Clockwise, ${135}^o$
• C. Counterclockwise, ${135}^o$
• D. Clockwise, ${45}^o$
  

Answer 1

The correct option is B Clockwise, ${135}^o$

Given:
$\angle F{E}_{1}E={45}^o$
Observing the figure, we can conclude that side $BC$ of $ABCD$ corresponds to side $FG$ of $EFGH$.
So, to get the angle by which $ABCD$ has been rotated around $(0,0)$ to obtain $EFGH$, we have to calculate the angle between side $BC$ and side $FG$ around $(0,0)$, i.e., $\angle B{E}_{1}F$.
We know that $\angle B{E}_{1}F+\angle F{E}_{1}E={180}^o$
$\angle B{E}_{1}F={180}^o-{45}^o={135}^o$
Now, counterclockwise rotation by ${135}^o$ will take rectangle $ABCD$ to the fourth quadrant, but $EFGH$ is in the first quadrant.
Therefore, the rectangle ABCD has been rotated clockwise by ${135}^{\circ }$ around (0, 0) to obtain image EFGH.