Answer:
Explanation:
To create a similar polygon from a pre-image, you can use one or more of the following transformations:
Scaling: Multiply the coordinates of each vertex of the pre-image by a scale factor to obtain the corresponding vertices of the similar polygon. This will change the size of the polygon but not its shape.
Translation: Move the pre-image by adding a fixed value to each coordinate of every vertex. This will shift the polygon horizontally and/or vertically.
Rotation: Rotate the pre-image by a certain angle around a fixed point. This will change the orientation of the polygon.
Here are some specific steps you can follow to create a similar polygon from a pre-image using one, two, or three of these transformations:
One transformation:
Scaling: Choose a scale factor and multiply the coordinates of each vertex of the pre-image by this factor.
Two transformations:
Scaling: Choose a scale factor and multiply the coordinates of each vertex of the pre-image by this factor.
Translation: Choose a vector and add this vector to each coordinate of every vertex of the scaled pre-image.
Three transformations:
Scaling: Choose a scale factor and multiply the coordinates of each vertex of the pre-image by this factor.
Rotation: Choose an angle and a fixed point, and rotate the scaled pre-image around this point by the chosen angle.
Translation: Choose a vector and add this vector to each coordinate of every vertex of the rotated pre-image.
Note that the order of the transformations matters. In general, scaling should be done first, followed by rotation, and then translation.