Flipping Across the Axis Reflection Flipping Across the Axis

What is reflection? A Reflection is an exact copy of the same image or picture that is flipped across an axis.

What does that mean in 6th grade math? When we use the coordinate plane, we need to find the reflection of points from one quadrant to another. Reflection is like drawing a picture on a piece of paper, folding it, tracing it, and seeing how the new picture looks.

What does that mean in 6th grade math? When we use the coordinate plane, we need to find the reflection of points from one quadrant to another. The coordinate plane is the sheet of paper. The first point is the picture you drew. The axis is where you fold the paper. The reflection is where the new drawing is. 5 4 3 2 1 We will reflect ‘pictures’ on the coordinate plane, but will keep it simple and just reflect points across the x axis & y axis!

Know the Signs of Each Quadrant! + - - - - + + + 5 4 3 2 1

Let’s see how it works! The language we use is “Reflect across the axis.” If it says reflect across the x-axis, then your new point will be on the other side of the x-axis. If it says reflect across the y-axis, other side of the y-axis. 5 4 3 2 1

What do you notice about the points? 5 4 3 2 1 (3, 4) The digits/numbers are the same. One of the signs are different The points are in a straight line. (3, -4)

What is the reflection of (-3, -4) across the x-axis? How does this work? What is the reflection of (-3, -4) across the x-axis? * Since (-3, -4) has a - -, it starts in Quadrant 3. * To reflect across the x-axis, the point has to go across the x-axis into another quadrant. * Rewrite the numbers from the first point (-3, -4)… take away the signs. * Starting in Quadrant 3 and moving across the x-axis moves the point into Quadrant 2. The signs for Quadrant 2 are -+, so add the signs -+ to the point. 5 4 3 2 1 ( ) - 3, - 4

Let’s practice! - + 5, - - 5 +- means start in Q4. Reflect (5, -5) across the y-axis! Steps to Follow: Write the coordinate pair for the first point. Figure out which Quadrant the point will go to when it crosses the y-axis. Change the signs of the pair to the new quadrant’s signs. - + 5, - - 5 +- means start in Q4. Cross the y-axis means end in Q3.

Let’s practice! + 5, - 5 +- means start in Q4. Cross the x-axis means Reflect (5, -5) across the x-axis! Steps to Follow: Write the coordinate pair for the first point. Figure out which Quadrant the point will go to when it crosses the x-axis. Change the signs of the pair to the new quadrant’s signs. + 5, - 5 +- means start in Q4. Cross the x-axis means end in Q1.

Let’s Try Without the Coordinate Plane When we do not have a coordinate plane, we use the quadrant signs to help us! Remember the Quadrant signs: Figure out which quadrant the point is in by looking at the signs of the numbers of the pair. You have to know which quadrant the point is in, so you will know which quadrant it’s going to. For example: (2, -3) has a +2 and a -3, so it’s +- +- means Quadrant 4. If reflecting across the x-axis, the point goes from Q4 to Q1 & the new point would be ++ or (2, 3). If reflecting across the y-axis, the point goes from Q4 to Q3 & the new point would be - - or (-2, -3). ++ -- -+ +-

(9, -3) Reflect across the x-axis! (9, -3) is + - Now (9, -3) becomes (9, 3)! The point is + -, so it starts in Q4. To cross the x-axis, the point goes to Q1 and becomes + +. ++ -- -+ +-

(-3, -6) Reflect across the x-axis! (-3, -6) is - - Now (-3, -6) becomes (-3, 6)! The point is - -, so it starts in Q3. To cross the x-axis, the point goes to Q2 and becomes - +. ++ -- -+ +-

(3, 6) Reflect across the y-axis! (3, 6) is + + Now (3, 6) becomes (-3, 6)! The point is + +, so it starts in Q1. To cross the y-axis, the point goes to Q2 and becomes - +. ++ -- -+ +-

(-1, -5) Reflect across the y-axis! (-1, -5) is - - Now (-1, -5) becomes (1, -5)! The point is - -, so it starts in Q3. To cross the y-axis, the point goes to Q4 and becomes + -. ++ -- -+ +-

You Try!! (-12, -3) (5, -9) (21, -1) (-2, -5) Reflect (12, -3) across the y-axis: Reflect (-5, -9) across the y-axis: Reflect (21, 1) across the x-axis: Reflect (-2, 5) across the x-axis: (-12, -3) (5, -9) (21, -1) (-2, -5)