Identify reflections, rotations, and translations

Learning Objectives Define and differentiate between reflections, rotations, and translations. Identify the type of rigid transformation that maps a pre-image to its image on a coordinate plane. Determine the line of reflection (x-axis, y-axis, y=x) given a pre-image and its reflected image. Identify the center (origin) and angle of rotation (90°, 180°, 270°) for a given rotated figure. Describe a translation using coordinate notation, such as (x, y) -> (x + a, y + b). Verify that reflections, rotations, and translations are isometries that preserve side lengths and angle measures. Ever wonder how animators make a character walk across the screen or a logo is flipped to create a perfect mirror image? 🎮 This tutorial explores the three fundamental rigid transformations:...

TermDefinitionExample Rigid Transformation (Isometry)A transformation that changes the position of a figure without changing its size or shape. It preserves distances, angle measures, and collinearity.Sliding a triangle 5 units to the right. The new triangle is congruent to the original. Pre-imageThe original figure before a transformation is applied.If triangle ABC is transformed, ABC is the pre-image. ImageThe resulting figure after a transformation has been applied.If triangle ABC is transformed into triangle A'B'C', then A'B'C' is the image. ReflectionA transformation that 'flips' a figure across a line, called the line of reflection, creating a mirror image. The orientation of the figure is reversed.Reflecting the point (3, 2) across the y-axis...

Translation Rule (x, y) \rightarrow (x + a, y + b) This rule describes a translation. Every point on the pre-image is moved 'a' units horizontally and 'b' units vertically. A positive 'a' means a shift right, negative is left. A positive 'b' means a shift up, negative is down. Common Reflection Rules Across x-axis: (x, y) \rightarrow (x, -y) \\ Across y-axis: (x, y) \rightarrow (-x, y) \\ Across line y=x: (x, y) \rightarrow (y, x) These rules show how the coordinates of a point change when reflected over the x-axis, y-axis, or the line y=x. Notice which coordinate changes sign or position. Rotation Rules about the Origin (0,0) 90° counter-clockwise: (x, y) \rightarrow (-y, x) \\ 180°: (x, y) \rightarrow (-x, -y) \\ 270° counter-c...