Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What does the term 'dilation' imply in matrix transformations?

Addition of values to coordinates
Reducing the dimensions of the matrix
Scaling the matrix by a specified factor
Rotating the matrix about an axis

The correct answer is: Scaling the matrix by a specified factor

The term 'dilation' in the context of matrix transformations specifically refers to the process of scaling the matrix by a specified factor. When dilation occurs, each point in the matrix is moved away from or toward a fixed point (usually the origin), proportionally based on the scaling factor. This means that if you apply a dilation transformation, the overall size of the figure represented by the matrix changes without altering its shape, preserving the relative proportions between the points. In mathematical terms, if you have a matrix representing a geometric figure, a dilation can be represented by multiplying every coordinate of the matrix by a positive scalar factor. A factor greater than one expands the figure, while a factor less than one will shrink it. This understanding is crucial in geometric transformations, particularly in fields like computer graphics and geometry.