1. Warm Up 1. Reflect the preimage using y=x as the line of reflection given the following coordinates: A(-2, 4), B(-4, -2), C(-5, 6)

2. Translations G.CO.A.2 Represent transformations in the plane, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

3. Translations Translation Theorem A translation is an isometry.

4. Example 1: Translate the following figure using the given coordinate. Coordinate Notation: (x,y) →(x-3,y+4)

5. Investigation – Transformations on a Coordinate Plane Step 1 – On graph paper, create and label four sets of coordinate axes. Draw the same polygon in the same position in a quadrant of each of the four graphs. Write one of these ordered pair rules below each graph. a. (x, y) →(-x, y) b. (x, y) →(x, -y) c. (x, y) →(-x, -y) d. (x, y) →(y, x) You will need: 1.graph paper 2.patty paper

6. Step 2 – Use the ordered pair rule you assigned to each graph to relocate the vertices of your polygon and create its image. Step 3 – Use patty paper to see if your transformation is a reflection, translation, or rotation. Compare your results with those of your group. Complete the conjecture. Be specific.

7. Coordinate Transformations Conjecture a. The ordered pair rule (x, y) →(-x, y) is a _____________. b. The ordered pair rule (x, y) →(x, -y) is a ______________. c. The ordered pair rule (x, y) →(-x, -y) is a ______________. d. The ordered pair rule (x, y) →(y, x) is a ______________. reflection across the y-axis reflection across the x-axis rotation about the origin reflection across the y=x

8. Minimum Distance Let’s explore on Geometer Sketchpad.

9. Finding Minimum Distance Imagine you have been stranded on an island for the past three weeks. You have built yourself a hut off the beach just into the woods. One day you are walking in the woods collecting food and you notice your hut in the distance is on fire! All of your survival supplies are stored in your hut! Your only chance to save the hut is to run to the beach, fill up your bucket with water and run to the hut to put out the fire and hopefully save your supplies!

10. Refer to the diagram below… ________________________________ Ocean

11. Hurry your hut is on FIRE!!! Hut(5, 1) You(-1, 5) Ocean: x-axis