F L I P P I N G AC R O S S T H E A X I S

REFLECTION

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

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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

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3

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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,then your new point will be on the

other side of the y-axis.

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WHAT DO YOU NOTICE ABOUT THE POINTS?

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(3, 4)

(3, -4)

1) The digits/numbers are the same.

2) One of the signs are different

3) The points are in a straight line.

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, thepoint has to go across the x-axis into another quadrant.

* Rewrite the numbers from the firstpoint (-3, -4)… take away the signs.

* Starting in Quadrant 3 and movingacross the x-axis moves the point intoQuadrant 2. The signs for Quadrant 2 are -+, so add the signs -+ to the point.

( )

HOW DOES THIS WORK?

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-3, 4-

LET’S PRACTICE!

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!

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 + -.

++---+

+-

1) Reflect (12, -3) across the y-axis:

2) Reflect (-5, -9) across the y-axis:

3) Reflect (21, 1) across the x-axis:

4) Reflect (-2, 5) across the x-axis:

YOU TRY!!

(-12, -3)

(5, -9)

(21, -1)

(-2, -5)