Reflections: graph the image (Tutorial Only)

Learning Objectives Graph the image of a point or polygon after a reflection across the x-axis. Graph the image of a point or polygon after a reflection across the y-axis. Graph the image of a point or polygon after a reflection across the line y = x. Graph the image of a point or polygon after a reflection across the line y = -x. Graph the image of a polygon after a reflection across any given horizontal line (y = k). Graph the image of a polygon after a reflection across any given vertical line (x = h). Apply coordinate rules to determine the vertices of a reflected image without graphing. Ever wonder how a mirror creates a perfect, flipped copy of you? 🤔 That's a reflection, and we can map it precisely on a coordinate plane! In this tutorial, you will learn how t...

TermDefinitionExample ReflectionA transformation that flips a figure across a line, called the line of reflection. Each point in the original figure is the same distance from the line of reflection as its corresponding point in the reflected figure.If point P(3, 2) is reflected across the y-axis, its image is P'(-3, 2). Pre-imageThe original figure before a transformation is applied.In a reflection, if triangle ABC is the starting figure, it is the pre-image. ImageThe new figure that results from applying a transformation to the pre-image. The image is often denoted with prime notation (e.g., A').If triangle ABC is reflected to create triangle A'B'C', then A'B'C' is the image. Line of ReflectionThe fixed line over which a figure is flipped. It acts...

Reflection across the x-axis R_{x-axis}: (x, y) \rightarrow (x, -y) To reflect a point across the x-axis, keep the x-coordinate the same and negate the y-coordinate. Reflection across the y-axis R_{y-axis}: (x, y) \rightarrow (-x, y) To reflect a point across the y-axis, negate the x-coordinate and keep the y-coordinate the same. Reflection across the line y = x R_{y=x}: (x, y) \rightarrow (y, x) To reflect a point across the line y = x, swap the x- and y-coordinates. Reflection across the line y = -x R_{y=-x}: (x, y) \rightarrow (-y, -x) To reflect a point across the line y = -x, swap the x- and y-coordinates and negate both of them.