Reflection, rotation, and translation

Learning Objectives Identify and describe the three basic types of geometric transformations: reflection, rotation, and translation. Distinguish between a pre-image and its image after a transformation. Perform a translation of a 2D shape on a coordinate grid. Perform a reflection of a 2D shape across a horizontal or vertical line on a coordinate grid. Perform a rotation of a 2D shape 90 degrees clockwise or counter-clockwise around a given point on a coordinate grid. Describe the transformation that maps a pre-image to its image. Recognize real-world examples of reflections, rotations, and translations. Have you ever looked in a mirror and seen your reflection? 🪞 Or watched a Ferris wheel spin around? 🎡 These are all examples of how shapes and objects can move in mathem...

TermDefinitionExample TransformationA transformation is a way to move a geometric shape from one position to another without changing its size or shape. It's like picking up a shape and putting it down somewhere else.Sliding a book across a table is a transformation. Pre-imageThe pre-image is the original shape before any transformation is applied.If you draw a triangle, that's your pre-image. ImageThe image is the new shape created after a transformation has been applied to the pre-image. It's the 'after' picture.The triangle after you slide it to a new spot is the image. TranslationTranslation is a transformation where a shape slides from one position to another without turning or flipping. Every point of the shape moves the same distance in the same direction.S...

Translation Rule To translate a point $(x, y)$ by 'a' units horizontally and 'b' units vertically, the new point will be $(x+a, y+b)$. This rule tells you how to slide every point of a shape. If 'a' is positive, move right; if negative, move left. If 'b' is positive, move up; if negative, move down. Reflection Rule (Across X-axis) To reflect a point $(x, y)$ across the x-axis, the new point will be $(x, -y)$. When reflecting across the x-axis, the x-coordinate stays the same, and the y-coordinate changes its sign (flips from positive to negative, or negative to positive). Imagine folding the paper along the x-axis. Reflection Rule (Across Y-axis) To reflect a point $(x, y)$ across the y-axis, the new point will be $(-x, y)$. Wh...