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Geometry Transformations

Geometry reflection

A reflection is a "flip" of an object over a line. Let's look at two very common reflections: a horizontal reflection and a vertical reflection.

 Horizontal Reflection (flips across) Vertical Reflection (flips up/down)

How to draw the reflection of a plane figure

 Label the vertices of the original figure as A, B, C,.... Draw a perpendicular line from the mirror line to each of the vertices. (The distance line should be at a right angle to the mirror line). Extend the line from the vertices to the opposite side of the mirror line by the same distance. Mark the position of the new vertices. Draw lines to join the new vertices. Label the points of the reflected image as A', B', C',...

A reflection in a line produces a mirror image in which corresponding points on the original shape are always the same distance from the mirror line.

The reflected image has the same size as the original figure, but with a reverse orientation.

Examples of transformation geometry in the coordinate plane...

• Reflection over y-axis:     (x, y) $\rightarrow\;$ (-x, y)

• Reflection over x-axis:     (x, y) $\rightarrow\;$ (x, -y)

• Reflection over line y = x:  (x, y) $\rightarrow\;$ (y, x)

 Transform ABCD according to the rule (x, y) $\rightarrow\;$ (-x, y)

Solution:
A(0, 6) $\rightarrow\;$ A'(0, 6)
B(5, 6) $\rightarrow\;$ B'(-5, 6)
C(4, 2) $\rightarrow\;$ C'(-4, 2)
D(2, 2) $\rightarrow\;$ D'(-2, 2)

Graphically:

 Reflect over the line x=2
Solution:

 Find the minimal path from P to l , to point S.

Solution: