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?
Thats wrong bot
wrong again!
Just change the sign of each coordinate. So (-6,4) → (6,-4)
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, 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).
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).