Reflections: graph the image (Tutorial Only)

Learning Objectives Define reflection, pre-image, image, and line of reflection. Identify the line of reflection given a pre-image and its reflected image. Graph the reflection of a point across the x-axis or y-axis. Graph the reflection of a polygon across the x-axis or y-axis. Graph the reflection of a point or polygon across a horizontal or vertical line. Describe the relationship between a pre-image and its reflected image (congruence). Have you ever looked in a mirror and seen your exact copy, just flipped? 🪞 That's a reflection, and in math, we can do the same with shapes on a graph! In this tutorial, you'll learn how to 'flip' points and shapes across a line on a coordinate plane to create their reflected images. Understanding reflections helps u...

TermDefinitionExample ReflectionA transformation that 'flips' a figure over a line, creating a mirror image. Each point in the original figure is the same distance from the line as its corresponding point in the reflected figure.Flipping a triangle over the x-axis to get a new triangle below it. Pre-imageThe original figure or point before a transformation is applied.If point A is at (2, 3), then A is the pre-image. ImageThe new figure or point created after a transformation has been applied. It is often denoted with a prime symbol (').If point A is reflected to A', then A' is the image. Line of ReflectionThe line over which a figure is reflected. It acts like a mirror.The x-axis, the y-axis, or a line like y=2 or x=-3. Coordinate PlaneA two-dimensional plane form...

Reflection Across the x-axis If a point $(x, y)$ is reflected across the x-axis, its image is $(x, -y)$. The x-coordinate stays the same, and the y-coordinate changes to its opposite. This means the point moves vertically across the x-axis. Reflection Across the y-axis If a point $(x, y)$ is reflected across the y-axis, its image is $(-x, y)$. The y-coordinate stays the same, and the x-coordinate changes to its opposite. This means the point moves horizontally across the y-axis. Reflection Across a Horizontal Line ($y=k$) If a point $(x, y)$ is reflected across a horizontal line $y=k$, its image is $(x, 2k-y)$. The x-coordinate stays the same. To find the new y-coordinate, calculate the distance from the point to the line $y=k$, and then move that same distance on th...