The point P(3,3) is rotated 270 degrees counterclockwise around the origin. What are the coordinates of the resulting point, P’?
The point F(
–
4,
–
1) is rotated 270° counterclockwise around the origin.
Well, it must be doing some yoga moves! Okay, let me calculate the coordinates for you.
To rotate a point around the origin counterclockwise, we use the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, theta = 270 degrees. Now let's plug in the values:
x' = 3 * cos(270) - 3 * sin(270) = -3
y' = 3 * sin(270) + 3 * cos(270) = -3
So, the coordinates of the resulting point, P', are (-3, -3). Voila!
To find the coordinates of the resulting point, P', after rotating point P(3,3) 270 degrees counterclockwise around the origin, you can use the following steps:
1. Visualize the initial point, P(3,3), and the origin on a coordinate plane.
2. To rotate a point counterclockwise around the origin, you can use the following formula:
P'(x', y') = (x * cosθ - y * sinθ, x * sinθ + y * cosθ)
In this formula, (x, y) are the coordinates of the initial point, (x', y') are the coordinates of the resulting point, and θ is the angle of rotation.
3. Substitute the values into the formula:
P'(x', y') = (3 * cos270 - 3 * sin270, 3 * sin270 + 3 * cos270)
4. Simplify the equation using the following trigonometric identities:
cos270 = cos(360 - 270) = cos90 = 0
sin270 = sin(360 - 270) = sin90 = 1
P'(x', y') = (3 * 0 - 3 * 1, 3 * 1 + 3 * 0)
= (0 - 3, 3 + 0)
= (-3, 3)
Therefore, the coordinates of the resulting point, P', are (-3, 3).
The point A (3,2) is rotated 270 degrees counterclockwise about the origin and is then reflected over the y- axis. What is the ordered pair for point A?
(x,y) -> (y,-x)
so, what do you think?