Algebra 4-2 Transformations on the Coordinate Plane (3, – 2) III Q (0, 1) J (1, 4) & S (1, 0) (– 3, – 2) ) Math Pacing Harbour

In geometry, a transformation is a way to change the position of a figure.

REFLECTION

A REFLECTION IS FLIPPED OVER A LINE. A reflection is a transformation that flips a figure across a line. A REFLECTION IS FLIPPED OVER A LINE.

After a shape is reflected, it looks like a mirror image of itself. REFLECTION Remember, it is the same, but it is backwards After a shape is reflected, it looks like a mirror image of itself. A REFLECTION IS FLIPPED OVER A LINE.

A REFLECTION IS FLIPPED OVER A LINE. The line of reflection can be on the shape or it can be outside the shape. Notice, the shapes are exactly the same distance from the line of reflection on both sides. The line that a shape is flipped over is called a line of reflection. Line of reflection A REFLECTION IS FLIPPED OVER A LINE.

reflectional symmetry. Sometimes, a figure has reflectional symmetry. This means that it can be folded along a line of reflection within itself so that the two halves of the figure match exactly, point by point. Basically, if you can fold a shape in half and it matches up exactly, it has reflectional symmetry.

REFLECTIONAL SYMMETRY An easy way to understand reflectional symmetry is to think about folding. What happens when you unfold the piece of paper? Do you remember folding a piece of paper, drawing half of a heart, and then cutting it out?

REFLECTIONAL SYMMETRY Line of Symmetry Reflectional Symmetry means that a shape can be folded along a line of reflection so the two haves of the figure match exactly, point by point. The line of reflection in a figure with reflectional symmetry is called a line of symmetry. The two halves are exactly the same… They are symmetrical. The two halves make a whole heart.

REFLECTIONAL SYMMETRY The line created by the fold is the line of symmetry. How can I fold this shape so that it matches exactly? A shape can have more than one line of symmetry. Where is the line of symmetry for this shape? I CAN THIS WAY NOT THIS WAY Line of Symmetry

REFLECTIONAL SYMMETRY How many lines of symmetry does each shape have? 3 4 5 Do you see a pattern?

REFLECTIONAL SYMMETRY Which of these flags have reflectional symmetry? United States of America Canada No England No Mexico

Reflections on a Coordinate Plane Performing reflections on a coordinate plane. The x-axis and y-axis will be our lines of reflections. You have to count the spaces on the coordinate plane in order to determine the distance between a point and the line of reflection.

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

T T’ J’ J Y’ Y 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’ Name the coordinates of the reflected object: J 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?

R P D U U’ U’’ D’ D’’ P’’ P’ R’’ R’ 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?