Reflections What are reflections?

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

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

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

Reflection Over the x-axis Graph the trapezoid: A(-4, 4) B(-1, 5) C(-1, 1) D(-4, 2) C A B D B’B’ D’D’ A’A’ C’C’ A’(-4, -4) B’(-1, -5) C’(-1, -1) D’(-4, -2) Observations: Figures are CONGRUENT. Y values change to the opposite. 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

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

What do we know about reflections so far? The figures are CONGRUENT. This means they are the same size and shape. 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. 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. 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?! 1. 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

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) A B C Using the mirror, place it on the Line y =x. Then look through The mirror to reflect the points. A’A’ B’B’ C’C’ A’(2, -4) B’(-1, -3) C’(-2, -5) What do you notice About the coordinate Points?

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)

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

Practice Problems

Solution to Problem 1

Problem Two

Solution to Problem 2

Problem Three

Solution to Problem Three

Practice Problem 4

Solution to Problem 4

Practice Problem 5

Solution to Problem 5

Homework

Homework Solution