How to translate, rotate, and reflect geometric shapes.
Cartesian coordinate systems: This is the system that uses x and y axes to plot points on a graph.
Translation: Moving an object from one position to another while maintaining its size and shape.
Reflection: Flipping an object over a line to create a mirror image.
Rotation: Turning an object around a fixed point by a certain angle.
Scaling: Changing the size of an object by multiplying each coordinate by a scale factor.
Composite transformations: Applying multiple transformations in succession to achieve a desired result.
Isometries: Transformations that preserve distance and angle measure, such as translations, reflections, and rotations.
Similarity transformations: Transformations that preserve shape but not necessarily size, such as scaling.
Transformations in higher dimensions: Extending the concepts of transformations to three or more dimensions.
Applications of transformations: Using transformations to solve real-world problems and applications in fields such as engineering, physics, and computer graphics.
Translation: This is a type of transformation that moves every point of a figure the same distance and direction.
Reflection: This is a type of transformation that flips a figure across a line or a plane.
Rotation: This is a type of transformation that turns a figure around a fixed point. The angle of rotation is measured in degrees.
Dilation: This is a type of transformation that changes the size of a figure. Dilation can either enlarge or shrink the size of the figure.
Shearing: This is a type of transformation that stretches or compresses a figure along an axis. This type of transformation is also called distortion.
Stretching: This is a type of transformation that elongates a figure along an axis. This type of transformation is often used in animations.
Compression: This is a type of transformation that shortens a figure along an axis. This type of transformation is often used in animations.
Inversion: This is a type of transformation that turns a figure inside out. This type of transformation is often used in computer graphics.
Combination: This is a type of transformation that combines two or more transformations together. This type of transformation is often used in 3D modeling.
Affine transformation: This is a type of transformation that preserves straight lines, parallelism, and ratios of distances between points. This type of transformation is often used in computer vision and machine learning.