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>