Holt Geometry

12-2 Translations

Identify and draw translations.

Objective

Holt Geometry

12-2 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.

Holt Geometry

12-2 Translations

Example 1: Identifying Translations

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

No; the figure appears to be flipped.

Yes; the figure appears to slide.

A. B.

Holt Geometry

12-2 Translations

Check It Out! Example 1

Tell whether each transformation appears to be a translation.

a. b.

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

Yes; all of the points have moved the same distance in the samedirection.

Holt Geometry

12-2 Translations

Holt Geometry

12-2 Translations

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.

Holt Geometry

12-2 Translations

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 ofthe vertices.

Holt Geometry

12-2 Translations

Holt Geometry

12-2 Translations

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).

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

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

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

Graph the preimage and the image.

Holt Geometry

12-2 Translations

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).

R(2, 5) R’(2 – 3, 5 – 3) = R’(–1, 2)

S(0, 2) S’(0 – 3, 2 – 3) = S’(–3, –1)

T(1, –1) T’(1 – 3, –1 – 3) = T’(–2, –4)

U(3, 1) U’(3 – 3, 1 – 3) = U’(0, –2)

Graph the preimage and the image.

R

S

T

UR’

S’

T’

U’

Holt Geometry

12-2 Translations

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)

Holt Geometry

12-2 Translations

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>