A quadrilateral with vertices G(−10,1) , E(−6,−4) , O(2,0) , and M(0,4) is rotated about the origin 270 degrees (counterclockwise). Apply rotation mapping rules to find the image of M .(1 point) M′ (,)
To rotate a point counterclockwise about the origin by an angle of 270 degrees, we can use the following rotation mapping rule:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
where (x, y) is the original point, (x', y') is the new image point, and θ is the angle of rotation.
In this case, the original point M is (0, 4) and the angle of rotation is 270 degrees.
Using the rotation mapping rule:
(x', y') = (0*cos270 - 4*sin270, 0*sin270 + 4*cos270)
= (0 - (-4), 0 + 0)
= (4, 0)
Therefore, the image of M is M' (4, 0).
To find the image of point M after rotating the quadrilateral 270 degrees counterclockwise about the origin, we can apply the rotation mapping rules.
The rotation mapping rule for a counterclockwise rotation of 270 degrees about the origin is:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image point, and θ is the angle of rotation.
Let's apply this rule to point M(0, 4) when rotating 270 degrees counterclockwise:
x' = 0 * cos(270°) - 4 * sin(270°)
y' = 0 * sin(270°) + 4 * cos(270°)
Since cos(270°) = 0 and sin(270°) = -1, we can simplify the equations:
x' = -4 * (-1) = 4
y' = 0 * 0 + 4 * 0 = 0
Therefore, the image of point M after rotating the quadrilateral 270 degrees counterclockwise about the origin is M'(4, 0).
To find the image of point M after rotating the quadrilateral 270 degrees counterclockwise about the origin, we can use the rotation mapping rules.
The rotation mapping rule for a counterclockwise rotation of θ degrees about the origin is given by:
(x', y') = (x * cos(θ) - y * sin(θ), x * sin(θ) + y * cos(θ))
Here, θ = 270 degrees. Let's calculate the image of point M(0, 4) using this rule:
x' = (0 * cos(270) - 4 * sin(270)) = (0 - (-4)) = 4
y' = (0 * sin(270) + 4 * cos(270)) = (0 + 0) = 0
So, the image of point M after rotating the quadrilateral 270 degrees counterclockwise about the origin is M' (4, 0).