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This guide explores the concept of reflections in coordinate geometry, detailing the line of reflection and the rules for various transformations. It defines how to find images of points when reflected over the x-axis, y-axis, and lines such as y=x or y=-x. Examples provide clarity, demonstrating how specific points are transformed, highlighting that reflections are isometric transformations maintaining congruence. Practice with a worksheet is included to reinforce understanding of reflection rules.
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Reflections Section 9.3
Line of Reflection • The mirror line that an image is reflected over.
Coordinate Rule for Reflections • If (a,b) is reflected over the x-axis, its image is the point (a, -b) • If (a,b) is reflected over the y-axis, its image is the point (-a, b)
Coordinate Rule for Reflections • If (a,b) is reflected over the line y = x, its image is the point (b, a) • If (a,b) is reflected over the line y = -x, its image is the point (-b, -a)
Coordinate Rule for Reflections • If the point (4, 7) was reflected over the line y = x, what would be its image? • If the point (2, -5) was reflected over the x-axis, what would be its image? • If the point (-3, 6) was reflected over the y-axis, what would be its image? • If the point (-8, -3) was reflected over the line y = -x, what would be its image?
Reflection • A reflection is an isometry (congruence transformation).
Homework • Reflections Worksheet
