Rule For Reflection Across Y Axis, Understand the formulas for reflection over the x-axis, y-axis, the origin, and line y=x, and see graphs with examples. The reflections are shown in Figure 9. Together, we will work through several examples of how to perform a reflection over the x axis and y axis. To reflect the graph of a function h(x) over the x -axis (that is, to flip the graph upside-down), multiply the function by −1 to get −h(x). The preimage above has been reflected across he y -axis. Khan Academy does not support this browser. Learn the reflection rules for the x-axis, y-axis, and the line y = x: which coordinate changes, why the rules work, worked examples, and practice. Unsupported browser Upgrade your browser Explore Reflect over the x-axis: When you reflect a point across the x -axis, the x- coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Example: Reflect the triangle with vertices (1,2), (4,2), and (2,5) over the y-axis. Learn reflection in Y axis with definition formula rules and solved examples for coordinate geometry problems and exam practice. Most Common Types of Reflections Reflection over the x-axis A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A'. Scroll down the page for more examples and solutions of reflection on the coordinate plane. Rotations can be achieved by performing two composite reflections over intersecting lines. Reflect over the x-axis: When you reflect a point across the x -axis, the x- coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). You can describe the reflection in words, or with the following notation: ry − axis(x, y) → (− x, y) Jan 21, 2020 · Reflection Over Y Axis When reflecting over (across) the y-axis, we keep y the same, but make x-negative. Reflection Across the Y-Axis: y = f (-x) This lesson explains how to reflect a function across the y-axis using y equals f of negative x. To reflect the graph of a function h(x) around the y -axis (that is, to mirror the two halves of the graph), multiply the argument of the function by −1 to get h(−x). If you forget the rules for reflections when graphing, simply fold your paper along the x -axis (the line of reflection) to see where the new figure will be located. For a point reflection, we actually reflect over a specific point, usually that point is the origin . See how an equation would be reflected over the y-axis and x-axis with graph examples. This means, all of the x -coordinates have been multiplied by -1. The general rule for a reflection over the x-axis: Learn how to reflect over the x-axis and y-axis. For example, if you have point A (3, 4), its reflection about the y-axis becomes A' (-3, 4). Worked examples plus a free practice question. . Note: Want to see how to reflect a figure over the y-axis? Then this tutorial was made for you! In this tutorial, you'll see how to use coordinates from the original figure to reflect the figure over the y-axis. May 16, 2025 · Algebraic Rules for y-axis Reflection Reflecting a function or a point across the y-axis conforms to straightforward algebraic rules that streamline the transformation process. A vertical reflection reflects a graph vertically across the $x$ -axis, while a horizontal reflection reflects a graph horizontally across the $y$ -axis. The resulting rotation will be double the amount of the angle formed by the intersecting lines. Take a look! The following diagram show the coordinate rules for reflection over the x-axis, y-axis, the line y = x and the line y = -x. Jun 15, 2022 · A reflection is an example of a transformation that takes a shape (called the preimage) and flips it across a line (called the line of reflection) to create a new shape (called the image). 2 days ago · The most common lines of reflection are the x -axis, the y -axis, or the lines y = x or y = − x. To use Khan Academy you need to upgrade to another web browser. Sep 17, 2020 · This video shows the Reflection Rules with examples for reflection across the x-axis, y-axis, y=x, and y=-x. Learn about reflection rules in math. Oct 24, 2025 · The mathematical rule for reflection over y axis follows the pattern (x, y) → (-x, y). Apr 9, 2025 · This free tutorial for students will teach you how to construct points and figures reflected over the x axis and reflected over the y axis. Khan Academy Khan Academy Reflecting shapes Reflecting shapes: diagonal line of reflection Reflecting shapes Reflect shapes Math> High school geometry> Performing transformations> Mar 30, 2015 · On this lesson, you will learn how to perform reflections over the x-axis and reflections over the y-axis (also known as across the x-axis and across the y-a A point reflection is just a type of reflection. Just select one of the options below to start upgrading. In standard reflections, we reflect over a line, like the y-axis or the x-axis. Sep 28, 2026 · The shape's reflection is formed by connecting the reflected points in the same order as the original shape. By examining the coordinates of the reflected image, you can determine the line of reflection. It covers the coordinate mapping rule, step-by-step algebraic substitution, and worked examples with a quadratic and a square root function so you can see how both the graph and the domain change. Learn how to reflect points and figures over the x-axis and y-axis with the rules (x, -y) and (-x, y). zeaj, nu9w, eisc, c7, ia53r, euopgp, aytroboa, oo5, 8khod, nikb,