Question

Points A and B are rotated along the circumference of the given circle to get points A' and B' in the following manner:
Point A: ${180}^{\circ }$ clockwise rotation
Point B: ${90}^{\circ }$ counterclockwise rotation
Which of the following options represents the correct coordinates of the points A and B after the given rotations?

Statement 1:
The correct coordinates of points A and B after the given rotations are: A'(−3, −4) and B'(0, 5)
Statement 2: Arcs AB and A'B' have the same length.

• A. Only statement 1 is correct.
• B. Both the statements are incorrect.
• C. Both the statements are correct.
• D. Only statement 2 is correct.

Answer 1

The correct option is A Only statement 1 is correct.

Given: Point A is rotated by ${180}^{\circ }$ in the clockwise direction.
The given transformation is illustrated in the image shown below.

From the above figure, we can observe that the coordinates of point A' are (-3, -4).
Given: Point B is rotated by ${90}^{\circ }$ in the counterclockwise direction.
The given transformation is illustrated in the image shown below.
From the above figure, we can observe that the coordinates of point B' are (0, 5).
Now, the positions of points A, B, A', and B' are shown in the image given below.

From the given image, we can clearly say that arcs AB and A'B' do not have the same length.
$\to$ Option A is correct.