The Dilations exercise used to appear under the Geometry Math Mission, but was apparently removed. This exercise explores dilations about a point.
Types of Problems[]
There are two types of problems in this exercise:
- Construct the image and answer the questions: This problem has a coordinate plane with a figure and describes a dilation. The user is asked to construct the image under the dilation and answer several questions associated with the transformation.
Construct the image and answer the questions
- Determine the dilation: This problem has a pre-image and image under a particular dilation. The user is asked to find the center and magnitude of the dilation that is pictured.
Determine the dilation
Strategies[]
Knowledge of vocabulary terms and a discerning geometric eye are encouraged to ensure success on this exercise.
- Dilations are a similitude. The preserve angle measure, but not necessarily Euclidean length.
- An efficient way to dilate is to move from the center to a particular point or vertex of the preimage. Then multiply the number of spots moved by the scale factor. This new number is the number of spots the image will be from the center.
- To find the center on Determine the dilation, choose a convenient point on the image that goes through a grid point and follow it back to the preimage. Once this is done for two points, it will point at the center of the dilation. The magnitude is the multiple that is done against the preimage length to get the image length.
Real-life Applications[]
- A firm understanding of transformations is necessary for understanding some of the more intricate concepts in non-Euclidean geometry (a possible model of the universe).
- Transformations have applications in art and architecture.
- Geometry, specifically trigonomery, is essential to make buldings from houses to tall skyscrapers.