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Identify and draw translations.PowerPoint Presentation

Identify and draw translations.

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Identify and draw translations.

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Objective

Identify and draw translations.

A translation is a transformation where all the points of a figure are moved the same distance in the same direction. A translation is an isometry, so the image of a translated figure is congruent to the preimage.

Example 1: Identifying Translations

Tell whether each transformation appears to be a translation. Explain.

A.

B.

No; the figure appears to be flipped.

Yes; the figure appears to slide.

Check It Out! Example 1

Tell whether each transformation appears to be a translation.

a.

b.

Yes; all of the points

have moved the same

distance in the same

direction.

No; not all of the points have moved the same distance.

Example 2: Drawing Translations

Copy the quadrilateral and the translation vector. Draw the translation along

Step 1 Draw a line parallel to the vector through each vertex of the triangle.

Example 2 Continued

Step 2 Measure the length of the vector. Then, from each vertex mark off the distance in the same direction as the vector, on each of the parallel lines.

Step 3 Connect the images of

the vertices.

D(–3, –1) D’(–3 + 3, –1 – 1) = D’(0, –2)

E(5, –3) E’(5 + 3, –3 – 1) = E’(8, –4)

Example 3: Drawing Translations in the Coordinate Plane

Translate the triangle with vertices D(–3, –1), E(5, –3), and F(–2, –2) along the vector <3, –1>.

The image of (x, y) is (x + 3, y – 1).

F(–2, –2) F’(–2 + 3, –2 – 1) = F’(1, –3)

Graph the preimage and the image.

R(2, 5) R’(2 – 3, 5 – 3)

= R’(–1, 2)

R

S

R’

S(0, 2) S’(0 – 3, 2 – 3)

= S’(–3, –1)

U

S’

T(1, –1) T’(1 – 3, –1 – 3)

= T’(–2, –4)

T

U’

U(3, 1) U’(3 – 3, 1 – 3)

= U’(0, –2)

T’

Check It Out! Example 3

Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) along the vector <–3, –3>.

The image of (x, y) is (x – 3, y – 3).

Graph the preimage and the image.

Lesson Quiz: Part II

Translate the figure with the given vertices along the given vector.

3.G(8, 2), H(–4, 5), I(3,–1); <–2, 0>

G’(6, 2), H’(–6, 5), I’(1, –1)

4.S(0, –7), T(–4, 4), U(–5, 2), V(8, 1); <–4, 5>

S’(–4, –2), T’(–8, 9), U’(–9, 7), V’(4, 6)

Lesson Quiz: Part III

5. A rook on a chessboard has coordinates (3, 4). The rook is moved up two spaces. Then it is moved three spaces to the left. What is the rook’s final position? What single vector moves the rook from its starting position to its final position?

(0, 6); <–3, 2>