Reflections What are reflections Sue Beck Unit 1

Reflections What are reflections? Sue Beck Unit 1 Math

What are the characteristics of a reflection? n n n A reflection is a mirror image of the original shape. This means it looks the same, except that it is flipped! A reflected figure is congruent to its original shape.

How do we reflect a figure over the y-axis? So, A’ should Be 4 units away From the y-axis! 4 units away 2 units A 4 units away B’ 2 units A’ B Plot ΔABC: A(-4, 4) B(-2, 4) C(-4, 1) What are the Coordinates Of ΔA’B’C’? C 4 units away A’(4, 4) Observations: B’(2, 4) 1. Both triangles are congruent C’(4, 1) 2. The reflected figure is the mirror image of the original. 3. The reflected figure flipped over to the right. 4. The x coordinate switch to the opposite value.

Reflection over the y – axis. 4 units Coordinates Of ΔA’B’C’: 4 units A A’ Graph the ΔABC: A(-4, 2) B(-3, -1) C(-5, -2) A’ (4, 2) B’(3, -1) C’(5, -2) C B 3 units 5 units B’ 3 units 5 units C’

Reflection Over the x-axis Observations: Graph the trapezoid: A(-4, 4) A’(-4, -4) B A • Y values change to the B(-1, 5) B’(-1, -5) C(-1, 1) C’(-1, -1) D(-4, 2) D’(-4, -2) • Figures are CONGRUENT. opposite. D D’ A’ C C’ B’ • The distance from the line of reflection stays the same for each shape: Example: C is 1 unit from the x-axis C’ is 1 unit from the x-axis

Reflecting over the X-axis A Graph the ΔABC: A(3, 6) A’(3, -6) B(-6, -1) B’(-6, -1) C(5, 1) B’ C C’(5, -1) C’ B A’

What do we know about reflections so far? n n n The figures are CONGRUENT. This means they are the same size and shape. Distance from the line of reflection stays the same. For example, if point A is 2 units from the reflection line, then A’ is also 2 units from that line. It is only going in the opposite direction. The reflected figure is the mirror image of the original shape. It is only flipped.

Example #1: Reflect the object below over the x-axis: Name the coordinates of the original object: A: (-5, 8) A B: (-6, 2) D C: (6, 5) D: (-2, 4) Name the coordinates of the reflected object: A’: (-5, -8) C B B’ B’: (-6, -2) D’ C’: (6, -5) C’ D’: (-2, -4) A’ How were the coordinates affected when the object was reflected over the x-axis?

Example #2: Reflect the object below over the y-axis: Name the coordinates of the original object: T: (9, 8) T T’ J: (9, 3) Y: (1, 1) J’ Name the coordinates of the reflected object: T’: (-9, 8) J Y’ Y J’: (-9, 3) Y’: (-1, 1) How were the coordinates affected when the object was reflected over the y-axis?

Example #3: Reflect the object below over the x-axis and then the y-axis: Name the coordinates of the original object: R: (-9, 9) R P: (-8, 5) P D: (-2, 4) U: (-9, 2) Name the coordinates of the reflected object: R’’: (9, -9) D U Would it make a difference if we reflected over the y -axis first and then the x-axis? Try it! Then reflect about what you discovered. U’ U’’ P’’: (8, -5) D’ D’’: (2, -4) D’’ P’ P’’ U’’: (9, -2) R’ How were the coordinates affected when the object was reflected over both the x-axis and y-axis? R’’