1

Reflections

2

Real-life reflections

AnimationArchitectureGraphic Design

3

ReflectionsA reflection creates a mirror image of each

point of a figure.

• A reflection is a transformation, an operation that changes a figure into another figure. The new figure created is called the image.• Notation: A A' is read “A goes to A prime”. 4

3

2

1

-2 -1 0 1 2

• AA' •

4

ReflectionTell whether the red figure is a reflection of the blue

figure.

This figure is a reflection. This figure is not a

reflection.

ReflectionsA reflection is a transformation in which a

figure is flipped over a line of reflection. This line can be thought of as a mirror in which the image is a reflection of the pre-image.

For this class, our line of reflection will be either the x-axis or the y-axis on a coordinate grid.

Reflecting a Polygon1. Determine the line of reflection (x or y axis).2. Find the distance from the vertex of the

polygon to the line of reflection.3. Mark the image of the vertex the same

distance from the line of reflection, but in the opposite direction.

4. Continue steps 2-3 until all vertices have been reflected.

5. Draw the image by drawing line segments connecting adjacent vertices.

Example

8

Reflecting in the y-Axis

http://staff.argyll.epsb.ca/jreed/math9/strand3/transformations.htm

Coordinates of each vertex of the triangle

and its image.Pre-image Image

Notice that when a point is reflected over the y-axis, its x-coordinate is multiplied by -1.

Preimage Image

(-3, -2) (3, -2)(-10, 0) (10, 0)(-2, 3) (2, 3)

9

Reflecting in the x-AxisCoordinates of each vertex of the triangle

and its image.

Pre-image Image

Notice that when a point is reflected over the x-axis, its y-coordinate is multiplied by -1.

(-2, 2) (-2, -2)(-1, 7) (-1, -7)(6, 5) (6, -5)

ConjectureA proposition or conclusion that is based on

limited evidence.

Example: Bats have wings and can fly. Eagles have wings and can fly. A Pegasus has wings and can fly. Conjecture: Any animal with wings can fly.

11

ReflectionsReflection across the x-axisWords To reflect a point across the x-axis,

multiply its y-coordinate by -1.Pre-image Image

Algebra (x, y) (x, -y)

Reflection across the y-axisWords To reflect a point across the y-axis,

multiply its x-coordinate by -1.Pre-image Image

Algebra (x, y) (-x, y)

12

Your turn!

Graph the triangle with

vertices J(0, 1), K(1, 4),

and L( 5, 2). Reflect

the triangle in the y-

axis.

13

Your turn!

Graph the quadrilateral

with vertices S(-3,2),

T(-1, 4), U(-4, 5), and

V(-5, 3). Reflect the

quadrilateral in the x-

axis.