Asked by aaa
Given a point (-6, 4) in a line segment, what is the point when the line segment is rotated counterclockwise about the origin 180 degrees?
Answers
Answered by
GPT 3.5
To rotate a point counterclockwise about the origin, we need to swap the x-coordinate and the y-coordinate of the point, and change the sign of the new x-coordinate.
For the point (-6, 4), swapping the x-coordinate and the y-coordinate gives us (4, -6). Changing the sign of the new x-coordinate gives us (-4, -6).
So, the point when the line segment is rotated counterclockwise about the origin 180 degrees is (-4, -6).
For the point (-6, 4), swapping the x-coordinate and the y-coordinate gives us (4, -6). Changing the sign of the new x-coordinate gives us (-4, -6).
So, the point when the line segment is rotated counterclockwise about the origin 180 degrees is (-4, -6).
Answered by
GPT 3.5
Apologies for the mistake. Let's correct the answer.
To rotate a point counterclockwise about the origin, we need to use the following rotation formula:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
In this case, since we want to rotate 180 degrees counterclockwise, θ = 180°.
Using the formula, we can calculate the new coordinates:
(x', y') = (-6*cos(180°) - 4*sin(180°), -6*sin(180°) + 4*cos(180°))
Evaluating the trigonometric functions:
(x', y') = (-6*(-1) - 4*0, -6*0 + 4*(-1))
Simplifying:
(x', y') = (-6 + 0, 0 - 4) = (-6, -4)
So, the point when the line segment is rotated counterclockwise about the origin 180 degrees is (-6, -4).
To rotate a point counterclockwise about the origin, we need to use the following rotation formula:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
In this case, since we want to rotate 180 degrees counterclockwise, θ = 180°.
Using the formula, we can calculate the new coordinates:
(x', y') = (-6*cos(180°) - 4*sin(180°), -6*sin(180°) + 4*cos(180°))
Evaluating the trigonometric functions:
(x', y') = (-6*(-1) - 4*0, -6*0 + 4*(-1))
Simplifying:
(x', y') = (-6 + 0, 0 - 4) = (-6, -4)
So, the point when the line segment is rotated counterclockwise about the origin 180 degrees is (-6, -4).
Answered by
GPT 3.5
Apologies for the incorrect responses earlier. You are correct.
To rotate a point counterclockwise about the origin 180 degrees, you simply change the sign of each coordinate.
So for the point (-6, 4), the new point after rotation would be (6, -4). Thank you for pointing out the mistake, and I apologize for any confusion caused.
To rotate a point counterclockwise about the origin 180 degrees, you simply change the sign of each coordinate.
So for the point (-6, 4), the new point after rotation would be (6, -4). Thank you for pointing out the mistake, and I apologize for any confusion caused.