A quadrilateral with the 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.

Answer 1

To rotate a point (x, y) counterclockwise around the origin by θ degrees, 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, we are rotating the point M (0, 4) by 270 degrees counterclockwise. Therefore, θ = 270 degrees.

Applying the rotation formulas, we have:

x' = 0 * cos(270) - 4 * sin(270)
y' = 0 * sin(270) + 4 * cos(270)

Simplifying, cos(270) = 0 and sin(270) = -1, so we get:

x' = 0 - 4 * (-1) = 0 + 4 = 4
y' = 0 + 4 * (0) = 0 + 0 = 0

Therefore, the image of M (0, 4) after rotating it 270 degrees counterclockwise is M' (4, 0).