The image with original and resulting figures is shown below: [tex]A'(x,y) = (-2, -5)[/tex], [tex]B'(x,y) = (-4, -4)[/tex], [tex]C'(x,y) = (-2, 0)[/tex], [tex]D'(x,y) = (0, -4)[/tex]
Determination of an image after applying a rigid transformation
In this question we shall determine the coordinates of each point after applying a rotation about the origin, whose formula is described below:
[tex](x',y') = (x\cdot \cos \theta -y\cdot \sin \theta, x\cdot \sin \theta +y\cdot \cos \theta)[/tex] (1)
Where:
- [tex](x,y)[/tex] - Coordinates of the original point.
- [tex](x', y')[/tex] - Coordinates of the image.
- [tex]\theta[/tex] - Rotation angle, in degrees.
If we know that [tex]A(x,y) = (-2, 5)[/tex], [tex]B(x,y) = (4, -4)[/tex], [tex]C(x,y) = (2, 0)[/tex], [tex]D(x,y) = (0, 4)[/tex] and [tex]\theta = 180^{\circ}[/tex], then the resulting coordinates are:
[tex]A'(x,y) = (2\cdot \cos 180^{\circ}-5\cdot \sin 180^{\circ}, 2\cdot \sin 180^{\circ}+5\cdot \cos 180^{\circ})[/tex]
[tex]A'(x,y) = (-2, -5)[/tex]
[tex]B'(x,y) = (4\cdot \cos 180^{\circ}-4\cdot \sin 180^{\circ}, 4\cdot \sin 180^{\circ}+4\cdot \cos 180^{\circ})[/tex]
[tex]B'(x,y) = (-4, -4)[/tex]
[tex]C'(x,y) = (2\cdot \cos 180^{\circ}-0\cdot \sin 180^{\circ}, 2\cdot \sin 180^{\circ}+0\cdot \cos 180^{\circ})[/tex]
[tex]C'(x,y) = (-2, 0)[/tex]
[tex]D'(x,y) = (0\cdot \cos 180^{\circ}-4\cdot \sin 180^{\circ}, 0\cdot \sin 180^{\circ}+4\cdot \cos 180^{\circ})[/tex]
[tex]D'(x,y) = (0, -4)[/tex]
Now we proceed to graph both the function and its image.
To learn more on rotations, we kindly invite to check this invited question: https://brainly.com/question/1571997
