Graph (2,1) (4,2) (3,5) translated 270 degrees
To translate the coordinates (2,1), (4,2), and (3,5) by 270 degrees counterclockwise, we can use the rotation formula:
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
where theta is the angle of rotation.
First, let's convert 270 degrees to radians:
270 degrees * (π/180 degrees) = 3π/2
Now we can plug in the values and calculate the translated coordinates:
For (2,1):
x' = 2*cos(3π/2) - 1*sin(3π/2)
= -2
y' = 2*sin(3π/2) + 1*cos(3π/2)
= 1
So the translated coordinates for (2,1) are (-2,1).
For (4,2):
x' = 4*cos(3π/2) - 2*sin(3π/2)
= -4
y' = 4*sin(3π/2) + 2*cos(3π/2)
= 2
So the translated coordinates for (4,2) are (-4,2).
For (3,5):
x' = 3*cos(3π/2) - 5*sin(3π/2)
= -5
y' = 3*sin(3π/2) + 5*cos(3π/2)
= 3
So the translated coordinates for (3,5) are (-5,3).
The translated points are: (-2,1), (-4,2), and (-5,3).