Reflections: find the coordinates

Learning Objectives Algebraically find the coordinates of a point reflected across the x-axis. Algebraically find the coordinates of a point reflected across the y-axis. Algebraically find the coordinates of a point reflected across the line y = x. Algebraically find the coordinates of a point reflected across the line y = -x. Determine the coordinates of a polygon's vertices after a reflection by applying the appropriate rule to each vertex. Find the coordinates of a point reflected across any horizontal line (y=k) or vertical line (x=h). Ever wondered how video game developers create a perfect mirror image of a character in a digital lake? 🎮 It's all about the mathematics of reflections! In this tutorial, you will learn the specific rules for reflections, a typ...

TermDefinitionExample ReflectionA transformation that creates a mirror image of a figure. Each point in the original figure is the same distance from the line of reflection as its corresponding point in the new figure.If point A is 3 units above the x-axis, its reflection, A', will be 3 units below the x-axis. Line of ReflectionThe line that a figure is flipped across to create its mirror image. It acts as the 'mirror'.Common lines of reflection include the x-axis, the y-axis, and the line y = x. Pre-imageThe original figure before any transformation is applied.If we reflect triangle ABC, then triangle ABC is the pre-image. ImageThe new figure that results from applying a transformation to the pre-image. It is often denoted with prime notation (e.g., A').If we reflect...

Reflection across the x-axis P(x, y) \rightarrow P'(x, -y) When reflecting a point across the x-axis, the x-coordinate stays the same, and the y-coordinate becomes its opposite. Reflection across the y-axis P(x, y) \rightarrow P'(-x, y) When reflecting a point across the y-axis, the y-coordinate stays the same, and the x-coordinate becomes its opposite. Reflection across the line y = x P(x, y) \rightarrow P'(y, x) When reflecting a point across the line y = x, the x-coordinate and y-coordinate switch places. Reflection across the line y = -x P(x, y) \rightarrow P'(-y, -x) When reflecting a point across the line y = -x, the x-coordinate and y-coordinate switch places and both become their opposites.