The point
G
(
–
5
,
–
1
)
is rotated
180
°
counterclockwise around the origin. What are the coordinates of the resulting point,
G
'
?
-
10
-
8
-
6
-
4
-
2
2
4
6
8
10
-
10
-
8
-
6
-
4
-
2
2
4
6
8
10
x
y
G
To find the coordinates of the resulting point G' after rotating point G, we can use the formula for a 2D rotation around the origin.
The formula states that to rotate a point (x, y) counterclockwise around the origin by an angle θ, the new coordinates (x', y') can be determined as follows:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, the angle of rotation is 180° counterclockwise. We can convert this angle to radians by multiplying it by π/180:
θ = 180° * π/180 = π radians
Let's plug in the values for point G: (x, y) = (-5, -1), and for θ = π:
x' = -5 * cos(π) - (-1) * sin(π)
y' = -5 * sin(π) + (-1) * cos(π)
Now, we can simplify the trigonometric functions:
x' = -5 * (-1) - (-1) * 0
y' = -5 * 0 + (-1) * (-1)
x' = 5
y' = -1
Therefore, the coordinates of the resulting point G' after rotating G 180° counterclockwise around the origin are:
G' (5, -1)