Question

Given a point on a line segment (−4, 5) , what is the new point when the point is rotated counterclockwise about the origin 270 degrees?

Answer 1

wrong

Answer 2

To find the new point when a point is rotated counterclockwise about the origin, we can use the rotation formula:

(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the new point, and θ is the angle of rotation.

In this case, the original point is (-4, 5) and the angle of rotation is 270 degrees.

Plugging in these values into the rotation formula, we get:

x' = -4*cos270 - 5*sin270 = -4*0 - 5*(-1) = -5
y' = -4*sin270 + 5*cos270 = -4*(-1) + 5*0 = 4

Therefore, the new point when the point (-4, 5) is rotated counterclockwise about the origin 270 degrees is (-5, 4).

Answer 3

Apologies for the incorrect response. Let's correct the solution.

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

(x', y') = (x * cosθ - y * sinθ, x * sinθ + y * cosθ)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the new point, and θ is the angle of rotation.

In this case, the original point is (-4, 5), and we want to rotate it counterclockwise by 270 degrees.

To determine the new point, we substitute the values into the rotation formula:

x' = -4 * cos270 - 5 * sin270 = 4 * 0 - 5 * (-1) = 5
y' = -4 * sin270 + 5 * cos270 = -4 * (-1) + 5 * 0 = 4

Thus, the new point when the point (-4, 5) is rotated counterclockwise about the origin 270 degrees is (5, 4).