Transformations: Translations & Reflections EQ: What is the rule for translating objects on the coordinate plane?

Course 3 7-7 Transformations The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

Translate the triangle below by (8, 3). C B

Translate the figure below by (-6, -3). D E

When translating, just add the coordinates together! Without Graphing… Example: Triangle XYZ has vertices X(-1, 2), Y(2,3) and Z(3, -1). It is translated by (-2, -3) Try: Quadrilateral MNOP has vertices M(0,5), N(3,2), O(6, -4) and P(-1, -4). It is translated by (3, -7) When translating, just add the coordinates together!

7-7 Transformations Just one Vertex Course 3 7-7 Transformations Just one Vertex Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after a translation of 10 units left. y Find C’ A B C D A B C D 2 x C’(-3, 3) –2

Which figure is being reflected across the x-axis? The y-axis? REFLECTIONS! Which figure is being reflected across the x-axis? The y-axis?

Reflections Triangle XYZ is located at X(4,2), Y(4, 7), Z(9,2) 1. Plot the triangle on your paper. 2. Draw the triangle reflected over the x-axis. 3. Write the coordinates for your new triangle. 4. What happened to your coordinates? -Discuss with a neighbor. -Can you come up with a rule? The x-coordinate stays the same, multiply the y-coordinate by -1 (x, y) --- (x, -y) (1, 2) --- (1, -2)

Now reflect the original triangle over the y-axis. What happened to the coordinates this time? What is the rule? The y-coordinate stays the same, multiply the x-coordinate by -1 (x, y) --- (-x, y) (1, 2) --- (-1, 2)

You try: Rectangle WXYZ has vertices W(-2, 3), X(4, 3), Y(4, -2) and Z(-2, -2). Reflect this over the x-axis. Do this without graphing! Homework… Handout