1. WARM UP 1 1. Graph ΔABC with the vertices A(–3, –2), B(4, 4), C(3, –3) 2. Graph ΔABC with the vertices D(1, 2), E(8, 8), F(7, 1) Compare the two graphs and write a few sentences describing the similarities and differences of the two triangles.

2. 2 Unit 2-Lesson 1 Unit 2:Transformations Lesson 1: Reflections and Translations

3. Objectives 3 I can identify and perform reflections and translations on a coordinate plane. I can predict the effect of a given ridged motion on a given figure. I can determine if two figures are congruent after a congruence transformation.

4. 4 Types of Transformations Reflections: These are like mirror images as seen across a line or a point. Translations ( or slides): This moves the figure to a new location with no change to the looks of the figure. Rotations: This turns the figure clockwise or counter-clockwise but doesn’t change the figure. Dilations: This reduces or enlarges the figure to a similar figure.

5. 5 Reflections You could fold the picture along line l and the left figure would coincide with the corresponding parts of right figure. l You can reflect a figure using a line or a point. All measures (lines and angles) are preserved but in a mirror image. Example:The figure is reflected across line l.

6. 6 Reflections – coordinates… reflects across the y axis to line n (2, 1)  (-2, 1) & (5, 4)  (-5, 4) Reflection across the x-axis: the x values stay the same and the y values change sign. (x, y)  (x, -y) Reflection across the y-axis: the y values stay the same and the x values change sign. (x, y)  (-x, y) Example:In this figure, line l : reflects across the x axis to line m. (2, 1)  (2, -1) & (5, 4)  (5, -4) ln m

7. 7 Reflections across specific lines: To reflect a figure across the line y = a or x = a, mark the corresponding points equidistant from the line. i.e. If a point is 2 units above the line its corresponding image point must be 2 points below the line. B(-3, 6)  B′ (-3, -4) C(-6, 2)  C′ (-6, 0) A(2, 3)  A′ (2, -1). Example: Reflect the fig. across the line y = 1.

8. 8 Lines of Symmetry If a line can be drawn through a figure so the one side of the figure is a reflection of the other side, the line is called a “line of symmetry.” Some figures have 1 or more lines of symmetry. Some have no lines of symmetry. One line of symmetry Infinite lines of symmetry Four lines of symmetry Two lines of symmetry No lines of symmetry

9. 9 translation vector – shows direction and distance of the “slide” VECTOR INTRODUCTION

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11. 11 Copy the figure and given translation vector. Then draw the translation of the figure along the translation vector. Step 1 Draw a line through each vertex parallel to vector. Step 2Measure the length of vector. Locate point G' by marking off this distance along the line through vertex G, starting at G and in the same direction as the vector. Step 3Repeat Step 2 to locate points H', I', and J' to form the translated image.

12. 12 Translations (slides) If a figure is simply moved to another location without change to its shape or direction, it is called a translation (or slide). A vector tells you how to translate a point or. If a point is moved “a” units to the right and “b” units up, then the translated point will be at (x + a, y + b). If a point is moved “a” units to the left and “b” units down, then the translated point will be at (x - a, y - b). A A′ A′ Image A translates to image A ′ by moving to the right 3 units and down 8 units. Example: A (2, 5)  B (2+3, 5-8)  A ′ (5, -3)

13. 13 Translations in the Coordinate Plane A. Graph ΔTUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector  –3, 2 .

14. 14 The vector indicates a translation 3 units left and 2 units up. (x, y)→(x – 3, y + 2) T(–1, –4)→(–4, –2) U(6, 2)→(3, 4) V(5, –5)→(2, –3)

15. 15 Translations in the Coordinate Plane B. Graph pentagon PENTA with vertices P(1, 0), E(2, 2), T(4, –1), and A(2, –2) along the vector  –5, –1 .

16. 16 The vector indicates a translation 5 units left and 1 unit down. (x, y)→(x – 5, y – 1) P(1, 0)→(–4, –1) E(2, 2)→(–3, 1) N(4, 1)→(–1, 0) T(4, –1)→(–1, –2) A(2, –2)→(–3, –3)

17. 17 A.A'(–2, –5), B'(5, 1), C'(4, –6) B.A'(–4, –2), B'(3, 4), C'(2, –3) C.A'(3, 1), B'(–4, 7), C'(1, 0) D.A'(–4, 1), B'(3, 7), C'(2, 0) A. Graph ΔABC with the vertices A(–3, –2), B(4, 4), C(3, –3) along the vector  –1, 3 . Choose the correct coordinates for ΔA'B'C'.

18. 18 B. Graph □GHJK with the vertices G(–4, –2), H(–4, 3), J(1, 3), K(1, –2) along the vector  2, –2 . Choose the correct coordinates for □G'H'J'K'. A.G'(–6, –4), H'(–6, 1), J'(1, 1), K'(1, –4) B.G'(–2, –4), H'(–2, 1), J'(3, 1), K'(3, –4) C.G'(–2, 0), H'(–2, 5), J'(3, 5), K'(3, 0) D.G'(–8, 4), H'(–8, –6), J'(2, –6), K'(2, 4)

19. 19 A. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 2 to position 3 in function notation and in words.