what is the new point when you rotate a geometric figure with (5, 8) 270 degrees counterclockwise about the origin?
To find the new point after rotating a geometric figure counterclockwise about the origin, we can use the rotation formula:
x' = x * cos(angle) - y * sin(angle)
y' = x * sin(angle) + y * cos(angle)
In this case, the original coordinates of the point are (5, 8), and we want to rotate it 270 degrees counterclockwise.
Converting 270 degrees to radians:
270 degrees = 270 * π/180 = 3π/2 radians
Using the rotation formulas:
x' = 5 * cos(3π/2) - 8 * sin(3π/2)
y' = 5 * sin(3π/2) + 8 * cos(3π/2)
Cos(3π/2) = 0
Sin(3π/2) = -1
x' = 5 * 0 - 8 * (-1)
x' = 0 + 8 = 8
y' = 5 * (-1) + 8 * 0
y' = -5 + 0 = -5
Therefore, the new point after rotating (5, 8) 270 degrees counterclockwise about the origin is (8, -5).
given a point on a line segment (-4, -6) what is the new point when the point is rotated clockwise about the origin 90 degrees?
To find the new point after rotating a point clockwise about the origin, we can use the rotation formula:
x' = x * cos(angle) + y * sin(angle)
y' = -x * sin(angle) + y * cos(angle)
In this case, the given point is (-4, -6), and we want to rotate it 90 degrees clockwise.
Converting 90 degrees to radians:
90 degrees = 90 * π/180 = π/2 radians
Using the rotation formulas:
x' = -4 * cos(π/2) + (-6) * sin(π/2)
y' = -(-4) * sin(π/2) + (-6) * cos(π/2)
Cos(π/2) = 0
Sin(π/2) = 1
x' = -4 * 0 + (-6) * 1
x' = 0 - 6 = -6
y' = 4 * 1 + (-6) * 0
y' = 4 + 0 = 4
Therefore, the new point after rotating (-4, -6) 90 degrees clockwise about the origin is (-6, 4).
rotate the point (5, 8) on a geometric figure 270 degrees clockwise. what is the new point?
To find the new point after rotating a point clockwise about the origin, we can still use the rotation formula:
x' = x * cos(angle) + y * sin(angle)
y' = -x * sin(angle) + y * cos(angle)
In this case, the given point is (5, 8), and we want to rotate it 270 degrees clockwise.
Converting 270 degrees to radians:
270 degrees = -270 * π/180 = -3π/2 radians
Using the rotation formulas:
x' = 5 * cos(-3π/2) + 8 * sin(-3π/2)
y' = -5 * sin(-3π/2) + 8 * cos(-3π/2)
cos(-3π/2) = 0
sin(-3π/2) = -1
x' = 5 * 0 + 8 * (-1)
x' = 0 - 8 = -8
y' = -5 * (-1) + 8 * 0
y' = 5 + 0 = 5
Therefore, the new point after rotating (5, 8) 270 degrees clockwise about the origin is (-8, 5).
rotate the new point (-4, -6) on a geometric figure 90 counterclockwise. what is the new point?
To find the new point after rotating a point counterclockwise about the origin, we can use the rotation formula:
x' = x * cos(angle) - y * sin(angle)
y' = x * sin(angle) + y * cos(angle)
In this case, the given point is (-4, -6), and we want to rotate it 90 degrees counterclockwise.
Converting 90 degrees to radians:
90 degrees = 90 * π/180 = π/2 radians
Using the rotation formulas:
x' = (-4) * cos(π/2) - (-6) * sin(π/2)
y' = (-4) * sin(π/2) + (-6) * cos(π/2)
Cos(π/2) = 0
Sin(π/2) = 1
x' = (-4) * 0 - (-6) * 1
x' = 0 + 6 = 6
y' = (-4) * 1 + (-6) * 0
y' = -4 + 0 = -4
Therefore, the new point after rotating (-4, -6) 90 degrees counterclockwise about the origin is (6, -4).