Reflections: find the coordinates

Learning Objectives Identify the pre-image and image of a reflection. 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. Determine the coordinates of a point reflected across the line y = -x. Apply reflection rules to find the coordinates of vertices of polygons. Describe the relationship between a pre-image and its reflected image. Ever looked in a mirror and seen an exact copy of yourself, just flipped? 🪞 That's a reflection! In this lesson, you'll learn how to mathematically describe these 'flips' on a coordinate plane, specifically focusing on how the coordinates of points change when reflected acro...

TermDefinitionExample ReflectionA transformation that 'flips' a figure over a line, creating a mirror image. The size and shape of the figure remain the same.Reflecting a triangle over the x-axis creates a new triangle that is a mirror image of the original. Pre-imageThe original figure or point before a transformation is applied.If point A is reflected to A', then A is the pre-image. ImageThe new figure or point after a transformation has been applied, often denoted with a prime symbol (e.g., A' for the image of A).If point A is reflected to A', then A' is the image. Line of ReflectionThe line over which a figure is reflected. Every point on the pre-image is the same perpendicular distance from this line as its corresponding point on the image.The x-axis can...

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. 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. 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 opposite signs.