Reflections: find the coordinates

Learning Objectives Identify the pre-image and image of a reflection. Define the line of reflection and its role in transformations. Determine the coordinates of a point reflected across the x-axis. Determine the coordinates of a point reflected across the y-axis. Determine the coordinates of a point reflected across the line y=x. Apply reflection rules to find the coordinates of vertices of a polygon. Ever looked in a mirror and noticed how everything is flipped? 🪞 In math, we call this a reflection! In this lesson, you'll learn how to mathematically describe these 'flips' on the coordinate plane. We'll explore how to find the exact new coordinates of points and shapes after they've been reflected across specific lines, which is a fundamental con...

TermDefinitionExample ReflectionA transformation that 'flips' a figure over a line, creating a mirror image. The size and shape of the figure remain unchanged.If you fold a piece of paper with a drawing on it and press down, the ink transfers to the other side, creating a reflection. Pre-imageThe original figure or point before a transformation is applied.If point A(2, 3) is reflected, A(2, 3) is the pre-image. ImageThe new figure or point after a transformation has been applied. It is often denoted with a prime symbol (e.g., A' for the image of A).If point A(2, 3) is reflected to A'(2, -3), then A'(2, -3) is the image. Line of ReflectionThe line over which a figure is reflected. Every point on the pre-image is the same distance from the line of reflection as its...

Reflection across the x-axis $(x, y) \rightarrow (x, -y)$ When a point is reflected across the x-axis, its x-coordinate remains the same, and its y-coordinate changes to its opposite sign. The x-axis acts as a mirror. Reflection across the y-axis $(x, y) \rightarrow (-x, y)$ When a point is reflected across the y-axis, its y-coordinate remains the same, and its x-coordinate changes to its opposite sign. The y-axis acts as a mirror. Reflection across the line y=x $(x, y) \rightarrow (y, x)$ When a point is reflected across the line y=x, the x and y coordinates swap their positions. Reflection across the line y=-x $(x, y) \rightarrow (-y, -x)$ When a point is reflected across the line y=-x, the x and y coordinates swap positions AND both change to their opposit...