What is the new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin?
To rotate a point (x, y) counterclockwise about the origin by an angle θ, the new coordinates can be calculated using the following formulas:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
In this case, the point is (5, 8) and the rotation angle is 270 degrees counterclockwise.
Converting 270 degrees to radians:
θ = 270 * (π/180) = 3π/2
Applying the formulas:
x' = 5*cos(3π/2) - 8*sin(3π/2) = 0 - (-8) = 8
y' = 5*sin(3π/2) + 8*cos(3π/2) = 5*(-1) + 8*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 rotate a point (x, y) clockwise about the origin by an angle θ, the new coordinates can be calculated using the following formulas:
x' = x*cos(θ) + y*sin(θ)
y' = -x*sin(θ) + y*cos(θ)
In this case, the point is (-4, -6) and the rotation angle is 90 degrees clockwise.
Converting 90 degrees to radians:
θ = 90 * (π/180) = π/2
Applying the formulas:
x' = -4*cos(π/2) + (-6)*sin(π/2) = 0 + (-6) = -6
y' = -(-4)*sin(π/2) + (-6)*cos(π/2) = 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 rotate a point (x, y) clockwise about the origin by an angle θ, the new coordinates can be calculated using the following formulas:
x' = x*cos(θ) + y*sin(θ)
y' = -x*sin(θ) + y*cos(θ)
In this case, the point is (5, 8) and the rotation angle is 270 degrees clockwise.
Converting 270 degrees to radians:
θ = 270 * (π/180) = 3π/2
Applying the formulas:
x' = 5*cos(3π/2) + 8*sin(3π/2) = 0 + 8 = 8
y' = -5*sin(3π/2) + 8*cos(3π/2) = -5*1 + 8*0 = -5
Therefore, the new point after rotating (5, 8) 270 degrees clockwise about the origin is (8, -5).
rotate (5,8) 270 degree clockwise
To rotate a point (x, y) clockwise about the origin by an angle θ, the new coordinates can be calculated using the following formulas:
x' = x*cos(θ) + y*sin(θ)
y' = -x*sin(θ) + y*cos(θ)
In this case, the point is (5, 8) and the rotation angle is 270 degrees clockwise.
Converting 270 degrees to radians:
θ = 270 * (π/180) = 3π/2
Applying the formulas:
x' = 5*cos(3π/2) + 8*sin(3π/2) = 5*0 + 8*(-1) = -8
y' = -5*sin(3π/2) + 8*cos(3π/2) = -5*(-1) + 8*0 = 5
Therefore, the new point after rotating (5, 8) 270 degrees clockwise about the origin is (-8, 5).
Rotate the point (5, 8) on a geometric figure 270 degrees clockwise. What is the new point?(1 point)
(8, −5)
(−8, 5)
(−8, −5)
(8, 5)
To rotate a point (x, y) 270 degrees clockwise about the origin, we can use the formula:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
In this case, the point is (5, 8) and the rotation angle is 270 degrees clockwise.
Converting 270 degrees to radians:
θ = 270 * (π/180) = 3π/2
Applying the formulas:
x' = 5*cos(3π/2) - 8*sin(3π/2) = 5*0 - 8*(-1) = 8
y' = 5*sin(3π/2) + 8*cos(3π/2) = 5*(-1) + 8*0 = -5
Therefore, the new point after rotating (5, 8) 270 degrees clockwise about the origin is (8, -5).
The correct answer is (8, -5).