What are reflections? Sue Beck

What are the characteristics of a reflection? 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 4 units away A 2 units 2 units B’ A’ B What are the Coordinates Of ΔA’B’C’? Plot ΔABC: A(-4, 4) B(-2, 4) C(-4, 1) C 4 units away 4 units away A’(4, 4) Observations: B’(2, 4) 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. The x coordinate switch to the opposite value.

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

Reflection Over the x-axis Observations: Graph the trapezoid: A(-4, 4) B(-1, 5) C(-1, 1) D(-4, 2) B A’(-4, -4) B’(-1, -5) C’(-1, -1) D’(-4, -2) Figures are CONGRUENT. A Y values change to the opposite. D C The distance from the line of reflection stays the same for each shape: Example: C is 1 unit from the x-axis C’ is1 unit from the x-axis C’ D’ A’ B’

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

What do we know about reflections so far? 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.

Reflecting over the line y=x First, what is the line y=x and how do we find it?! In order to graph a line, we need coordinate points. Which means we need a t-chart. Pick numbers to go in for your x values. 2. Then solve for the y values by substituting x into your equation y =x. X Y -3 -2 -1 1 2 3 -3 -2 -1 1 2 3

Draw the line y =x in the graph by plotting the points and highlight it! Graph the ΔABC: A(-4, 2) B(-3, -1) C(-5, -2) What do you notice About the coordinate Points? A’(2, -4) B’(-1, -3) C’(-2, -5) A B B’ C A’ Using the mirror, place it on the Line y =x. Then look through The mirror to reflect the points. C’

Reflect the following over the line y =x Graph the heart given the Following coordinates: A(4, - 6) B(7, -3) C(6, -1) D(5, -1) E(4, -2) F(3, -1) G(2, -1) H(1, -3) A’(-6, 4) B’(-3, 7) C’(-1, 6) D’(-1, 5) E’(-2, 4) F’(-1, 3) G’(-1, 2) H’(-3, 1)

Example #1: Reflect the object below over the x-axis: Name the coordinates of the original object: A A: (-5, 8) B: (-6, 2) D C C: (6, 5) D: (-2, 4) B Name the coordinates of the reflected object: A’: (-5, -8) 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 T’ T: (9, 8) J: (9, 3) Y: (1, 1) J’ J Name the coordinates of the reflected object: Y’ Y T’: (-9, 8) 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 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. R: (-9, 9) P: (-8, 5) P D D: (-2, 4) U: (-9, 2) U Name the coordinates of the reflected object: R’’: (9, -9) U’ U’’ P’’: (8, -5) D’ D’’ D’’: (2, -4) P’’ P’ U’’: (9, -2) R’’ R’ How were the coordinates affected when the object was reflected over both the x-axis and y-axis?

Practice Problems For the following problems, graph the reflection and state the coordinates.

Practice Problem One

Solution to Problem One

Problem Two

Solution to Problem Two

Problem Three

Solution to Problem Three

Practice Problem Four

Solution to Problem Four

Practice Problem Five

Solution to Problem Five