Geometric reflection is a transformation in geometry that flips a shape across an axis to produce a mirror image. This process involves changing the coordinates of a figure's vertices to create an image that is congruent to the original. Reflections can occur across the x-axis, y-axis, or diagonal lines like y = x and y = -x. The principles of reflection are observable in everyday life, such as in mirrors, water surfaces, and polished materials, where they demonstrate the spatial relationships in our environment.
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Reflection is a type of transformation that produces a mirror image of a shape
The axis of reflection is a line that functions as a mirror, with the original shape and its reflected image having congruent sizes and shapes but opposite orientations
The pre-image and reflected image are equidistant from the axis of reflection at corresponding points, maintaining this distance consistently across all points of the shape
Reflecting a figure over the x-axis involves changing the sign of the y-coordinates of each point in the figure
Reflecting a figure over the y-axis involves changing the sign of the x-coordinates of each point in the figure
Reflection over diagonal lines, such as y = x and y = -x, results in images that are both flipped and rotated 90 degrees with respect to the pre-image
Reflection can be observed in mirrors, where the mirror acts as the line of reflection
Reflection can also be seen on calm water surfaces, where the reflected image may vary due to ripples or waves
Reflection occurs on polished surfaces like glass or metal, where the angle of incidence equals the angle of reflection
Reflection maintains the size and shape of the original figure
The orientation of the reflected image is reversed compared to the pre-image
The distance from the axis of reflection is preserved for all corresponding points of the shape
00
The original figure and its reflection have identical ______ and sizes, but their orientations are ______.
shapes
opposite
01
Reflection across x-axis transformation rule
Transform (x, y) to (x, -y); y-coordinates sign changes.
02
Reflection across y-axis transformation rule
Transform (x, y) to (-x, y); x-coordinates sign changes.
