Rotating shapes Opens a modal. Determining rotations Opens a modal.
Rotations review Opens a modal. Determining reflections advanced Opens a modal. Reflecting shapes Opens a modal.
Reflections review Opens a modal. No videos or articles available in this lesson. Find measures using rigid transformations. Performing dilations Opens a modal. Properties and definitions of transformations.
Precisely defining rotations Opens a modal. This is called a vertex matrix. A square has its vertexes in the following coordinates 1,1 , -1,1 , -1,-1 and 1, If we want to create our vertex matrix we plug each ordered pair into each column of a 4 column matrix:. If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with.
When we want to create a reflection image we multiply the vertex matrix of our figure with what is called a reflection matrix.
The most common reflection matrices are:. To change the size of an object, scaling transformation is used. In the scaling process, you either expand or compress the dimensions of the object. Scaling can be achieved by multiplying the original coordinates of the object with the scaling factor to get the desired result.
- Homogenous Coordinates?
- Vector negation.
- Scalar vector operations.
If we provide values less than 1 to the scaling factor S, then we can reduce the size of the object. If we provide values greater than 1, then we can increase the size of the object.
Reflection is the mirror image of original object. In reflection transformation, the size of the object does not change.
The following figures show reflections with respect to X and Y axes, and about the origin respectively. A transformation that slants the shape of an object is called the shear transformation.