Understanding Dilation | A Fundamental Transformation in Mathematics

Dilation

Dilation is a transformation in mathematics that involves changing the size of a figure without altering its shape

Dilation is a transformation in mathematics that involves changing the size of a figure without altering its shape. It is a type of transformation that can be performed on two-dimensional and three-dimensional shapes.

In two-dimensional geometry, dilation involves stretching or shrinking a figure by a scale factor, which is a ratio that determines the relationship between the pre-image (original figure) and the image (transformed figure). The scale factor can be greater than 1 to create an enlargement or less than 1 to create a reduction. It can also be negative to reflect the figure across a line.

To perform a dilation, a center of dilation and a scale factor need to be specified. The center of dilation is a fixed point that remains unchanged during the transformation, while the scale factor determines the amount of change in the size of the figure. Each point of the original figure is moved in a straight line away from or towards the center of dilation, maintaining the same direction.

In three-dimensional geometry, dilation works similarly, but involves changing the size of a three-dimensional shape by multiplying the coordinates of each point by the scale factor.

Dilation is a fundamental concept in various areas of mathematics, including similarity, geometry, and transformations. It is particularly useful in analyzing and comparing shapes and understanding the relationship between different figures.

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