What is the new point when you rotate a geometric figure with point (5,8) 270 degrees counterclockwise about the orgin
To find the new point when you rotate a geometric figure with point (5,8) 270 degrees counterclockwise about the origin, we can use the rotation formula:
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
Here, x and y represent the original coordinates, and x' and y' represent the new coordinates after rotation. For a 270 degrees counterclockwise rotation, theta is equal to 270 degrees or (3/2)π radians.
Plugging in the values:
x' = 5*cos((3/2)π) - 8*sin((3/2)π)
y' = 5*sin((3/2)π) + 8*cos((3/2)π)
Using the trigonometric identities cos((3/2)π) = 0 and sin((3/2)π) = -1, we can simplify further:
x' = 5*0 - 8*(-1) = 8
y' = 5*(-1) + 8*0 = -5
Therefore, the new point after rotating (5,8) 270 degrees counterclockwise about the origin is (8, -5).
To rotate a point with coordinates (5,8) 270 degrees counterclockwise about the origin, we can use the rotation formula for a point (x, y) counterclockwise by angle θ around the origin:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, we are rotating 270 degrees counterclockwise, so θ = 270 degrees.
Let's substitute the values into the formulas:
x' = 5 * cos(270) - 8 * sin(270)
y' = 5 * sin(270) + 8 * cos(270)
To find the cosine and sine values for 270 degrees, we can use the following identities:
cos(270) = cos(360 - 90) = cos(90) = 0
sin(270) = sin(360 - 90) = sin(90) = 1
Substituting these values into the formulas:
x' = 5 * 0 - 8 * 1 = -8
y' = 5 * 1 + 8 * 0 = 5
Therefore, the new coordinates of the point (5,8) after rotating 270 degrees counterclockwise about the origin is (-8, 5).