rotation maps a segment with endpoints X (-6,2) and Y (-1, -3) onto a segment with endpoints X'(6, -2) and Y'(1,3). Which of the following rotations was performed?
(1 point)
• A rotation of 90° about the origin.
• A rotation of 180° about the origin.
• A rotation of 270° about the origin.
• A rotation of 360° about the origin.
To find the angle of rotation, we can use the formula:
angle of rotation = arctan((y2-y1)/(x2-x1))
Using the given points X (-6,2) and Y (-1,-3), we have:
angle of rotation = arctan((-3-2)/(-1+6))
This simplifies to:
angle of rotation = arctan(-5/5)
The angle of rotation is -45°.
To determine which rotation was performed, we need to compare the initial and final positions of the points. The segment XY is rotated to X'Y', so the rotation is clockwise.
Additionally, the segment XY is rotated to segment X'Y' about the origin. Since the angle of rotation is negative, the rotation is in the clockwise direction.
Therefore, the correct answer is:
• A rotation of 270° about the origin.