Reflections 1-4BWhat are transformations?

What are reflections?

What happened?Moved

Rotated

Enlarged

Transformation

A second figure that looks exactly like the first but is shifted, flipped, enlarged, shrunken or rotated.

Special Type of TransformationShe saw her reflection

in the mirror.

The trees were reflected in the lake.

The sphere was so clear, I saw my reflection.

Definition of Reflection

A reflection is a flipping of a figure over a line. This is the line of reflection. A reflection is a special type of transformation.

Line of Reflection

Pre-Image/Image

Pre-image the original figureImage the figure after a transformation

A

C

B A′B′

C′l

Pre-image (1) Image (2)

Pre-image/Image

To tell the two images apart, use prime notation A′.

When naming images of figures, list corresponding points in the same order.

Reflective Detective p. 68

Fold a sheet of paper in half. Poke the tip of a pencil through the folded paper at 3 points that are not collinear.

Open the paper and draw segments connecting the holes on each side of the fold. (You should have 2 triangles with the fold as the line of reflection.) Label all the points.

Draw segments connecting the points of the image with corresponding points of the pre-image. Measure the distance from the vertices to the fold. Measure the angles these segments make with the fold.

VocabularyEquidistant two points are the same distance

from another point, segment or line.Bisector a figure is cut into two

congruent halves.Perpendicular bisector a line or segment

that divides the segment into two congruent segments and is perpendicular to it.

A

l

B

l is a perpendicular bisector of AB

Perpendicular to a line construction p. 69

Use your paper from reflective detective to for your construction.

You will also need your compass and a ruler.

Definition

Point A′ is the reflection image over line l of point A if l is the perpendicular bisector of AA′.

l

A

A′

Assignment

p. 70, 1-10, 22-25