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9-2 Reflections

Explore the concept of reflections in mathematics through rules, examples, and practical applications. Learn how to reflect shapes and points across different axes and lines. Discover the transformations that maintain size and shape in rigid motions. Practice with exercises and find reflections of triangles across multiple lines.

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9-2 Reflections

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  1. 9-2 Reflections

  2. Key Concepts: • R stands for reflection and the Subscript tells you what to reflect on (ex: Rx-axis) • The “line of reflection” is what you reflect on • Reflection: keeps size and shape,it’s always a RIGID MOTION or ISOMETRY!!

  3. Just watch! Don’t need to write. • Rk = reflect over line k • Rl = reflect over line l l k

  4. Rx-axis Ry-axis Ry = x Ry =-x Example Original: (3,4) • (3,-4) • (-3,4) • (4,3) • (-4, -3)

  5. TOO • Graph each original • Find and graph the reflection across: • x-axis • y-axis • y = x • y = -x 1) (-2,-3) 2) (4,1) Answers: 1) (-2,3) (2,-3) (-3,-2) (3, 2) 2) (4,-1) (-4,1) (1,4) (-1, -4)

  6. Rules • Look at the answers that you got for the example and the 2 TOO. • Write mappings for reflecting across: • x-axis (x stays the same!) • y-axis (y stays the same!) • y = x (they flip flop, signs STAY) • y = -x (flip flop, signs CHANGE) But what about other lines????? • (x,y) → (x,-y) • (x,y)→ (-x,y) • (x,y)→ (y,x) • (x,y)→ (-y, -x)

  7. Point P has coordinates (3,4). What are the coordinates of:

  8. Reflections of Triangles

  9. Reflections over 2 lines:Find the image of Z(1, 1) after two reflections, first across line ℓ1, and then across line ℓ2. • ℓ1 : x = 2, ℓ2 : y-axis

  10. Homework • WS from: Pg. 557 # 7-14, 28-29, 32-34, 37

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