Translation

Pre - Requisite
Standard / 8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
CC Lesson / 8.2.1: Why Move Things Around?
8.2.2: Definition of Translation and Three Basic Properties
8.2.3: Translating Lines
Student Learning Goal / ·  Students perform translations of figures along a specific vector. Students label the image of the figure using appropriate notation.
·  Students learn that a translation maps lines to lines, rays to rays, segments to segments, and angles to angles.
Media / https://www.youtube.com/watch?v=-mOY2eWO2qw
Electric Slide – Marcia Griffiths
HW / #135
Spiral Review #32
WKSP

Rigid Motion

We will now focus on taking a figure and transforming it by either sliding, flipping or turning the figure.

·  The original point from the figure will be noted as a letter (let’s say P). The point’s ______. under a certain Function will be noted as F(P). Since F(P) is a result of P, we can say that P is to F(P).

·  We will be mapping figures on a (flat surface).

·  Rigid motions involve preserving size (aka ). In other words, the measurements on the original figure are the same as the measurements on the image produced from the original.

Example:

Explain what is done to the following original figure to get to each image below

Translation

There are three basic rigid motions. The first transformation we will be looking at is translation.

Place your transparency over the following example. Let’s map the lower left figure to the upper right figure.

We need to show both strength and direction.

·  Since we are starting at the lower left figure, we’re going to start at point A. Therefore, on your transparency, create an endpoint over point A.

·  Draw a straight segment to point A’s image, T(A). The segment you just created shows strength.

·  Since you are ending on T(A), place an arrowhead (on your transparency) above T(A). The arrowhead shows direction.

·  You’ve just created a vector!

Vector: a that has both (strength) and .

Example 1: A point

Map the following point according to its vector AB:

P .

Example 2: An angle

Map the following angle according to its vector DC:

Example 3: A figure

Map the following figure according to its vector EF:

There is a quicker way to write the notation of the points on the image. Instead of writing image of P as T(P), we can write the image of P as P’ (P prime).

Exercise:

1. / The diagram below shows figures and their images under a translation along HI. Use the original figures and the translated images to fill in missing labels for points and measures.

2. / Do translations preserve the length of segments?
3. / Do translations preserve the degree of angles?
4. / Translate the plane containing Figure A along AB.

5. / Draw each of the following. Then translate along the given vector TR.

a. an angle measuring 35°


What is the degree of the translated angle?
b. a segment with length 3cm
What is the length of the translated segment?
c. a point
d. a circle with radius 1in
What is the radius of the translated circle?
6. / In the diagram, ΔX’Y’Z’ is the image of ΔXYZ. Which type of transformation is shown?

a. reflection b. rotation c. translation d. dilation


Name: ______Date: ______

Pre-Algebra Exit Ticket

1. / Name the vector in the picture below.

2. / Name the vector along which a translation of a plane would map point A to its image T(A).

3. / Is Maria correct when she says that there is a translation along a vector that will map segment AB to segment CD? If so, draw the vector. If not, explain why not.

4. / Assume there is a translation that will map segment AB to segment CD shown above. If the length of segment CD is 8 units, what is the length of segment AB? How do you know?

Name: ______Date: ______


Pre-Algebra HW #135

1. / Translate the plane containing Figure B along BA.

2. / Translate point D along vector AB and label the image D’.

Will AB and DD' ever intersect?

Review

3. / Two lines meet at the common vertex of two rays. Set up and solve an equation to find the value of m.

4. / A circle has a radius of 2 cm.
a.  Find the exact area of the circular region.
b. Find the approximate area using 3.14 to approximate π.
5. / A stick is x meters long. A string is 4 times as long as the stick.
a.  Express the length of the string in terms of x.
b.  If the total length of the string and the stick is 15 meters long, how long is the string?