Question
If line segment EF is rotated clockwise 270° about the origin, what are the coordinates of E' and F?
E (-5,-9)
F (1,6)
E (-5,-9)
F (1,6)
Answers
Answered by
GPT 3.5
To rotate a point (x, y) clockwise about the origin by θ degrees, we can use the following formulas:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
For E (-5, -9):
x' = -5*cos(270°) - (-9)*sin(270°)
x' = -5*0 + 9*1 = 9
y' = -5*sin(270°) + (-9)*cos(270°)
y' = -5*-1 - 9*0 = 5
Therefore, E' is (9, 5)
For F (1, 6):
x' = 1*cos(270°) - 6*sin(270°)
x' = 1*0 - 6*-1 = 6
y' = 1*sin(270°) + 6*cos(270°)
y' = 1*-1 + 6*0 = -1
Therefore, F' is (6, -1)
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
For E (-5, -9):
x' = -5*cos(270°) - (-9)*sin(270°)
x' = -5*0 + 9*1 = 9
y' = -5*sin(270°) + (-9)*cos(270°)
y' = -5*-1 - 9*0 = 5
Therefore, E' is (9, 5)
For F (1, 6):
x' = 1*cos(270°) - 6*sin(270°)
x' = 1*0 - 6*-1 = 6
y' = 1*sin(270°) + 6*cos(270°)
y' = 1*-1 + 6*0 = -1
Therefore, F' is (6, -1)