Question

The given figure has a $\Delta PQR$ which is rotated and transformed to $\Delta P^{\prime }{Q}^{\prime }{R}^{\prime }$. Select the statement that holds true for the given transformation.

• A. Both B and C
• B. The angle of rotation $={90}^{\circ }$ about the origin and the rotation was done clockwise.
  
• C. The angle of rotation $={270}^{\circ }$ about the origin and the rotation was done clockwise.
  
• D. The angle of rotation $={90}^{\circ }$ about the origin and the rotation was done counterclockwise.
  

Answer 1

The correct option is A Both B and C

Let’s try to draw some conclusions based on the given figure shown in the graph.
The figure shown in the graph has undergone a transformation called rotation. Rotation involves turning the object at a particular angle considering a fixed point as the center of rotation. The number of degrees a figure rotates is known as the angle of rotation.

In the figure given above, $\Delta PQR$ is rotated ${90}^{\circ }$ counterclockwise about the origin and becomes P'Q'R'. So, the transformation involved in $\Delta PQR$ is rotation.


Also, moving $\Delta PQR$ in the clockwise direction for ${270}^{\circ }$ about the origin would end at the same place as moving ${90}^{\circ }$ in the counterclockwise direction.

So, we can say that the angle of rotation can be ${90}^{\circ }$ and ${270}^{\circ }$ in the clockwise and counterclockwise directions, respectively, both about the origin. That is, both options B and C are true here.

$\to$ Option D is correct.