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.
M’(?, ?)
To find the image of M after a 270-degree counterclockwise rotation about the origin, we can apply the rotation mapping rules:
For a point (x, y) rotated counterclockwise by angle θ about the origin, the new coordinates (x', y') can be found using the following formulas:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
In this case, the point M has coordinates (0, 4), and we want to rotate it 270 degrees counterclockwise.
Using the formulas above, we can calculate the new coordinates (x', y') as follows:
x' = 0*cos(270°) - 4*sin(270°)
= 0 - 4*(-1)
= 0 + 4 = 4
y' = 0*sin(270°) + 4*cos(270°)
= 0 + 4*(-1)
= 0 - 4 = -4
Therefore, the image of M after a 270-degree counterclockwise rotation about the origin is M'(4, -4).