Question

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 image of M.

Answer 1

To rotate a point (x, y) counterclockwise about the origin by a certain angle, we can use the following rotation mapping rules:

x' = x * cosθ - y * sinθ
y' = x * sinθ + y * cosθ

where (x', y') represents the coordinates of the image point after rotation, and θ represents the angle of rotation.

In this case, we need to rotate the point M(0, 4) about the origin 270 degrees counterclockwise. Let's apply the rotation mapping rules:

x' = 0 * cos270 - 4 * sin270
= 0 - (-4)
= 4

y' = 0 * sin270 + 4 * cos270
= 0 + 4
= 4

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