Mastering Reflections in Mathematics
Discover the art of reflecting shapes using mirror lines in this insightful guide that covers definitions, examples, and practical applications. Learn how to find images of points and shapes under reflections in various mirror lines. Enhance your understanding of geometry with step-by-step explanations and visual aids.
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05 July 2025 Reflections LO: To reflect shapes in using mirror lines. www.mathssupport.org
Reflections A reflectionis a transformation that flips a shape about a fixed line. This line is called the mirror line. The original shape is called the object. The reflected shape is called the image. A point on the object and its equivalent point on the image are equidistant from the mirror line . You need one thing to describe a reflection 1) the mirror line. www.mathssupport.org
Reflection Find the image of the point (4, 2) under a reflection in the x-axis. Draw the mirror line Draw a perpendicular line to the mirror line, check the distance. (4, 2) Draw a perpendicular line from the mirror line, opposite direction, same distance. This is the reflection of the point. (4, -2) www.mathssupport.org
Reflection Find the image A of the parallelogram A (1, 2), (6, 2), (7, 5), (2, 5), under a reflection in the line y= -1. Draw the mirror line (2, 5) (7, 5) A (6, 2) (1, 2) Measure the distance from each point to the mirror line, and from the mirror line to the image of the point. Plot the points and draw the image. This is the reflection of the parallelogram. (1, -4) (6, -4) A (2, -7) (7, -7) www.mathssupport.org
Reflection Find the image of the point (4, 2) under a reflection in the y-axis. Draw the mirror line Draw a perpendicular line to the mirror line, check the distance. (-4, 2) (4, 2) Draw a perpendicular line from the mirror line, opposite direction, same distance. This is the reflection of the point. www.mathssupport.org
Reflection Find the image B of the trapezium B (1, 2), (6, 2), (5, 5), (1, 5), under a reflection in the line x= -1. Draw the mirror line (-3, 5) (-7, 5) (1, 5) (5, 5) B B (6, 2) (-3, 2) (1, 2) (-8, 2) Measure the distance from each point to the mirror line, and from the mirror line to the image of the point. Plot the points and draw the image. This is the reflection of the trapezium. www.mathssupport.org
Reflection Find the image of the point (4, 2) under a reflection in the line y = x Draw the mirror line (2, 4) Draw a perpendicular line to the mirror line, check the distance. (4, 2) Draw a perpendicular line from the mirror line, opposite direction, same distance. This is the reflection of the point. www.mathssupport.org
Reflection (-2, 7) (1, 7) Find the image C of the triangle C (1, -2), (7, -2), (7, 1), under a reflection in the line y= x. C Draw the mirror line (7, 1) (-2, 1) Measure the distance from each point to the mirror line, and from the mirror line to the image of the point. Plot the points and draw the image. This is the reflection of the triangle. C (1, -2) (7, -2) www.mathssupport.org
Reflection Find the image of the point (4, 2) under a reflection in the line y = -x Draw the mirror line Draw a perpendicular line to the mirror line, check the distance. (4, 2) Draw a perpendicular line from the mirror line, opposite direction, same distance. This is the reflection of the point. (-2, -4) www.mathssupport.org
Reflection Find the image D of the triangle D (1, 1), (7, 1), (7, 4), under a reflection in the line y= -x. (7, 4) Draw the mirror line D (1, 1) (7, 1) Measure the distance from each point to the mirror line, and from the mirror line to the image of the point. Plot the points and draw the image. This is the reflection of the triangle. (-1, -1) D (-4, -7) (-1, -7) www.mathssupport.org
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