Reflections

1
Lesson 7.2

• Reflections

2
Lesson 7.2 Objectives

• Utilize reflections in a plane
• Define line symmetry
• Derive formulas for specific reflections in the
  plane

3
Reflections

• A transformation that uses a line like a mirror
  is called a reflection.
• The line that acts like a mirror is called the
  line of reflection.
• When you talk of a reflection, you must include
  your line of reflection
• A reflection in a line m is a transformation that
  maps every point P in the plane to a point P, so
  that the following is true
• If P is not on line m, then m is the
  perpendicular bisector of PP.
• If P is on line m, then PP.

4
Theorem 7.1Reflection Theorem

• A reflection is an isometry.
• That means a reflection does not change the shape
  or size of an object!

5
Line of Symmetry

• A figure in the plane has a line of symmetry if
  the figure can be mapped onto itself by a
  reflection in a line.
• What that means is a line can be drawn through an
  object so that each side reflects onto itself.
• There can be more than one line of symmetry, in
  fact a circle has infinitely many around.

6
Reflection Formula

• There is a formula to all reflections.
• It depends on which type of a line are you
  reflecting in.
• vertical
• horizontal
• y x

Vertical y-axis About x a
Horizontal x-axis About y a
y x
( x , y)
( -x 2a , y)
( x , -y 2a)
( y , x)