Answer:
(D). Therefore, the correct answer is
Explanation:
the other images. A rotation of 180 degrees clockwise about the point (1,2) means that every point on the blue object (D) will move to a new position that is 180 degrees away from the point (1,2) on a circle. The distance from the point (1,2) to the new position will be the same as the distance from the point (1,2) to the original position.
One way to find the new position is to use the formula:
(x′,y′)=(2x−x0,2y−y0)
where (x′,y′) is the new position, (x,y) is the original position, and (x0,y0) is the center of rotation. In this case, (x0,y0)=(1,2).
For example, let’s take the point (3, 4) on the blue object (D). Applying the formula, we get:
(x′,y′)=(2×3−1,2×4−2)
(x′,y′)=(5,6)
This means that the point (3, 4) on the blue object (D) will move to the point (5, 6) after the rotation.
We can repeat this process for all the points on the blue object (D) and see which image matches the new positions. Alternatively, we can use a visual method by drawing a line from each point on the blue object (D) to the point (1,2) and extending it until it reaches another point on the same circle. That point will be the new position after the rotation.
Using either method, we can see that none of the images match the rotation of the blue object (D). Therefore, the correct answer is: