Question
What are the coordinate of point E' if E (-9,1) is rotated 180° clockwise around the origin
Answers
GPT 3.5
To find the coordinates of point E' when point E is rotated 180° clockwise around the origin, we can use the formula for rotating a point in the coordinate plane:
The formula for rotating a point (x, y) counterclockwise by an angle θ around the origin is:
New x-coordinate: x' = x * cos(θ) - y * sin(θ)
New y-coordinate: y' = x * sin(θ) + y * cos(θ)
In this case, since we want to rotate E (-9, 1) 180° clockwise around the origin, θ would be π radians or 180°.
Using the formula with x = -9 and y = 1:
New x-coordinate: x' = -9 * cos(π) - 1 * sin(π) = -9 * (-1) - 1 * 0 = 9
New y-coordinate: y' = -9 * sin(π) + 1 * cos(π) = -9 * 0 + 1 * (-1) = -1
Therefore, the coordinates of point E' after rotating E (-9, 1) 180° clockwise around the origin are E' (9, -1).
The formula for rotating a point (x, y) counterclockwise by an angle θ around the origin is:
New x-coordinate: x' = x * cos(θ) - y * sin(θ)
New y-coordinate: y' = x * sin(θ) + y * cos(θ)
In this case, since we want to rotate E (-9, 1) 180° clockwise around the origin, θ would be π radians or 180°.
Using the formula with x = -9 and y = 1:
New x-coordinate: x' = -9 * cos(π) - 1 * sin(π) = -9 * (-1) - 1 * 0 = 9
New y-coordinate: y' = -9 * sin(π) + 1 * cos(π) = -9 * 0 + 1 * (-1) = -1
Therefore, the coordinates of point E' after rotating E (-9, 1) 180° clockwise around the origin are E' (9, -1).