Given a point on a line segment (-4, -6), what is the new point when the point is rotated clockwise about the origin 90 degrees?

Question

Generate a visually compelling abstract image dealing with geometric themes, without any text. As a reference, imagine an image containing geometric shapes such as line segments and points. One of these points should be represented with a specific emphasis, potentially denoted with a more prominent color or size, that sits on a line segment. The image will need to hint at a sense of movement or rotation, suggesting a 90-degree clockwise rotation around a central point, which is denoted as the origin, so include a center point to facilitate this. Keep the colors and the shapes abstract and professional, and include various angles for added complexity.

Given a point on a line segment (-4, -6), what is the new point when the point is rotated clockwise about the origin 90 degrees?

1. (-6, 4)
2. (4, 6)
3. (-6, -4)
4. (-4, 6)

Answer 1

To rotate a point clockwise about the origin, we can use the formula:

(x', y') = (x * cos(theta) + y * sin(theta), -x * sin(theta) + y * cos(theta))

In this case, since we want to rotate 90 degrees clockwise, we can plug in theta = -90 degrees or -pi/2.

(x', y') = (-4 * cos(-pi/2) + -6 * sin(-pi/2), -(-4) * sin(-pi/2) + -6 * cos(-pi/2))
(x', y') = (-4 * 0 + -6 * (-1), 4 * (-1) + -6 * 0)
(x', y') = (0 + 6, -4 + 0)
(x', y') = (6, -4)

Therefore, the new point after rotating (-4, -6) clockwise about the origin 90 degrees is (6, -4).

None of the answer choices match this result, so none of the answer choices are correct.

Answer 2

May you pick at least one answer bot please

Answer 3

Apologies for the incorrect initial response. Among the answer choices provided, the closest option to the correct answer is:

3. (-6, -4)