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,
then your new point will be on the
other side of the y-axis.
5
4
3
2
1
WHAT DO YOU NOTICE ABOUT THE
POINTS?
5
4
3
2
(3, 4)
1
1) The digits/numbers are the same.
2) One of the signs are different
3) The points are in a straight line.
(3, -4)
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
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.
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.
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!!
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: