Mannsplained.

Understanding geometry starts with understanding transformations. So what are transformations?

Rigid Transformations

We classify rigid transformations as geometric movements that change a figure’s position or orientation but NOT shape or size. Rigid transformations include:

• Translations
• Reflections
• Rotations

TRANSLATIONS

Translations are movements that “slide” shapes along a directed line or measurement. They do not change the figure’s shape, size, or orientation.

REFLECTIONS

Reflections flip figures over a specified line, each point is mapped to a direct mirror image of itself over the line.

ROTATIONS

Rotations turn figures around a specified point, known as the center of rotation. Figures are rotated by a certain angle.

In summary, all rigid transformations will move figures without altering their size or shape. Points will be mapped onto corresponding points and all shapes will remain congruent.

Non-rigid Transformations

Non-rigid transformations, unlike rigid transformations, change the size or shape of a figure. The altered figure will NOT be congruent to it’s original shape. Non-rigid transformations include:

• Dilations
• Shears

DILATIONS

Dilations are transformations which change the size of a figure, but not it’s shape, either enlarging or shrinking. Dilations require a center of dilation, basically the point each dilated point is connected to, and a scale factor, a positive number that represents the extent of the dilation.

For example, if your scale factor is 3, you multiply each coordinate of your original shape by 3 to get your dilated shape.

(1, 1) -> (3, 3)

SHEARS

Shears are transformations which “slide” points along a line parallel to a fixed line. A shear factor is used to determine the placement of the sheared figure.

Shear factor = Distance a point moves after shear/Perpendicular point distance from invariant line

Invariant line = The line in which points remain fixed

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