translations in the coordinate plane

Translations in the Coordinate Plane

Students will be able to predict the results of translations and draw translations on the coordinate plane.

Review

Introduction Video to Translations

http://www.youtube.com/watch?v=XdjH_EWhCZ0

VocabularyTransformation- maps one figure onto

anotherTranslation- the motion of moving a

figure without turning itCongruent Figures- same size and

shape, and the corresponding sides and angles have equal measures

Translations in the Coordinate Plane

Draw a Translation

Check Your Progress

Find Coordinates of a Translation

Check Your Progress

Triangle TUV has vertices T(6,-3), U(-2,0), and V(-1,2). Find the vertices of triangle T’U’V’ after a translation of 3 units right and 4 units down. Then graph the figure an its translated image.

Reflections in the Coordinate Plane

Students will be able to predict the results of a reflection and graph reflections on a coordinate plane.

Symmetry in Reflections

• Scientists have determined that the human eye uses symmetry to see. It is possible to understand what you are looking at even if you do not see all of it.

A, B, C, D…

• List all of the capital letters of the alphabet that look exactly the same when folded across a vertical line.

VocabularyLine Symmetry: Figures that match

exactly when folded in half have line symmetry.

Line Symmetry: Each fold line is called a line of symmetry.

Practice and Apply• Determine whether each figure

has line symmetry. If so, copy the figure and draw all lines of symmetry.

Practice and Apply• Copy each figure. Draw the

resulting figure when each figure is lipped over line.

Reflections in Nature

1. Does the size and shape remain the same on either side of the line of symmetry?

2. What do you notice about the distance from the points to the line of symmetry?

VocabularyReflection- A mirror imaged produced by flipping a figure over a line

Line of Reflection- The line in which an image is flipped to form a reflection

Image- the location or position of a figure after a transformation

How to draw a reflection

1. Count the units between a point and the line of reflection.

2. For each point (vertex), plot a point an equal distance away from the line of reflection on the reflected side

3. Connect the vertices to form the reflected image.

Example Reflect the image over the y-axis

You Try• Reflect the figure using the x

axis as a line of reflection.X (4, -4)Y (-2,-3)Z (2, -1)

What do you notice about the old coordinates and the new coordinates? Is there a pattern?

Discover the rule for the y-axisGraph triangle FGH with vertices

F (1,-1) G (5, -3), H (2, -4). Graph the image of triangle FGH after the reflection over the y axis.

Compare the new coordinates to the old coordinates to find your rule.

Reflecting Figures over axes

X-AxisThe x values remain the same, the y value changes signY-AxisThe y values remain the same, the x value changes the sign.

Exit Pass• Graph the figure with the given

vertices. Then graph the image of the figure after a reflection over the x-axis. Then graph the image after it has been translated up 2 units and right 3.

**Be sure to write the coordinates of the image’s vertices.