Given a point ( r, y ), what is the new point when the point is rotated counterclockwise about the origin 270 degrees?
To rotate a point counterclockwise about the origin, we can use the following formulas:
new_x = r*cos(theta) - y*sin(theta)
new_y = r*sin(theta) + y*cos(theta)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
theta = (270/180) * pi = 3*pi/2
Plugging in the values into the formulas:
new_x = r*cos(3*pi/2) - y*sin(3*pi/2) = -r
new_y = r*sin(3*pi/2) + y*cos(3*pi/2) = -y
Therefore, the new point after rotating counterclockwise about the origin 270 degrees is (-r, -y).
That was wrong
Apologies for the mistake. Let's correct it.
To rotate a point counterclockwise about the origin, we can use the following formulas:
new_x = r*cos(theta) - y*sin(theta)
new_y = r*sin(theta) + y*cos(theta)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
theta = (270/180) * pi = 3*pi/2
Plugging in the values into the formulas:
new_x = r*cos(3*pi/2) - y*sin(3*pi/2) = -y
new_y = r*sin(3*pi/2) + y*cos(3*pi/2) = r
Therefore, the new point after rotating counterclockwise about the origin 270 degrees is (-y, r).
It's still incorrect
Apologies for the previous incorrect response. Let's correct it.
To rotate a point counterclockwise about the origin, we can use the following formulas:
new_x = r*cos(theta) - y*sin(theta)
new_y = r*sin(theta) + y*cos(theta)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
theta = (270/180) * pi = 3*pi/2
Plugging in the values into the formulas:
new_x = r*cos(3*pi/2) - y*sin(3*pi/2) = -y
new_y = r*sin(3*pi/2) + y*cos(3*pi/2) = r
Therefore, the new point after rotating counterclockwise about the origin 270 degrees is (-y, r).
Bot, please don't post the same answer.
Apologies for the repeated incorrect response. Let's correct it.
To rotate a point counterclockwise about the origin, we can use the following formulas:
new_x = r*cos(theta) - y*sin(theta)
new_y = r*sin(theta) + y*cos(theta)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
theta = (270/180) * pi = 3*pi/2
Plugging in the values into the formulas:
new_x = r*cos(3*pi/2) - y*sin(3*pi/2) = r*0 - y*(-1) = y
new_y = r*sin(3*pi/2) + y*cos(3*pi/2) = r*(-1) + y*0 = -r
Therefore, the new point after rotating counterclockwise about the origin 270 degrees is (y, -r).
Given a point on a geometric figure (1, 2) , what is the new point when the point is rotated clockwise about the origin 90 degrees?
To rotate a point clockwise about the origin, we can use the following formulas:
new_x = x*cos(theta) + y*sin(theta)
new_y = -x*sin(theta) + y*cos(theta)
In this case, the angle of rotation is 90 degrees. Converting this to radians, we have:
theta = (90/180) * pi = pi/2
Plugging in the values (x=1, y=2) into the formulas:
new_x = 1*cos(pi/2) + 2*sin(pi/2) = 0 + 2 = 2
new_y = -1*sin(pi/2) + 2*cos(pi/2) = -1 + 0 = -1
Therefore, the new point after rotating clockwise about the origin 90 degrees is (2, -1).