1. Warm Up
Find the coordinates of the image of ∆ABC with vertices A(3, 4), B(–1, 4), and C(5, –2), after each reflection.
1. across the x-axis
2. across the y-axis
3. across the line y = x

2. Objective
Identify and draw translations.

3. 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.

4. 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.

5. 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.

6. 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.

7. A vector in the coordinate plane can be written as <a, b>, where a is the horizontal change and b is the vertical change from the initial point to the terminal (end) point.

9. 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.

10. The image of (x, y) is (x – 3, y – 3).
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) R S T U R’ S’ T’ U’
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.

11. Assignment
Pg. 614 (2-22 even)