Geometry – Transformations

In this lesson we going to learn: 
- Translation: Moving points and shapes in the coordinate plane
- Rotation: Rotating points and shapes around the origin
- Reflection: Flipping across different axes (and the origin)
- Dilation: Stretching shapes in one or two directions
- Preserving congruence: See which transformations keep things congruent
- Symmetry: When reflection or rotation doesn't change anything

Transformations are ways to move and manipulate geometric figures, in this section we focus on the coordinate grid.

Translating an entire shape means you are translating every point in the shape.

90-degree clockwise rotation (negative direction rotation) is finding the opposite of the x-coordinate, and reverse the coordinates (x, y) become (y, -x).

90-degree counterclockwise rotation (positive direction rotation) is finding the opposite of the y-coordinate, and reverse the coordinates (x, y) become (-y, x).

180-degree rotation is taking the opposite of both coordinates (x, y) become (-x, -y).

Reflection (x, y) across x-axis resulting (x, -y)

Reflection (x, y) across y-axis resulting (-x, y)

Reflection (x, y) across origin resulting (-x, -y)

Reflection (x, y) across y=x line resulting (y, x)

Dilation is stretching the same amount in perpendicular directions – change size, not overall shape or we can say dilation is a transformation that has a center and a scale factor with the center is a point and the scale factor given how much size stretches or shrinks.

Scale factor greater than 1, make shape(dilation) larger

Scale factor less than 1, make shape(dilation) smaller

There are for type of Symmetry: Line Symmetry, Rotational Symmetry, Point Symmetry, Planes of Symmetry

Geometry – Transformations | Translation | Rotation: 

Geometry – Transformations | Reflection | Dilation: 

Geometry – Transformations | Preserving congruence | Symmetry: