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```G.CO.A.5 STUDENT NOTES WS #7 –
1
We learn a lot about transformations when we analyze their motions in the coordinate plane. Patterns reveal
shortcuts/rules that allow us to quickly determine the coordinates of an image.
REFLECTION ON THE COORDINATE GRID
4
Reflection over
the y axis.
B (-1,3)
B' (1,3)
A (-3,2)
B (-x,y)
B' (x,y)
2
A' (3,2)
2
When we reflect over
the y axis, the y
values are
unchanged and the x
values are negated
(opposite).
C (-2,-1)
C' (2,-1)
RULE FOR REFLECTION OVER THE Y AXIS ry axis ( x, y)  ( x, y)
4
Reflection over
the x axis.
B (-2,3)
B (x,y)
2
When we reflect over
the x axis, the x
values are
unchanged and the y
values are negated
(opposite).
2
A (-5,2)
C (-1,1)
5
5
C' (-1,-1)'
A' (-5,-2)
2
2
B' (x,-y)
B' (-2,-3)
RULE FOR REFLECTION OVER THE X AXIS
Reflection over
the y = x line.
rx axis ( x, y )  ( x,  y )
E (2,6)
6
F (x,y)
When we reflect over
the y = x line, the x
and y values are
reversed.
F (3,5)
4
D (0,4)
F' (5,3)
F' (y,x)
2
E' (6,2)
D' (4,0)
5
RULE FOR REFLECTION OVER THE Y = X LINE ry  x ( x, y )  ( y, x)
G.CO.A.5 STUDENT NOTES WS #7 –
2
ROTATION ON THE COORDINATE GRID
4
Rotation of 90
When we rotate 90
see that the x and y
coordinates are
reversed and the new
x coordinate is
negated.
B (2,4)
C' (-y,x)
4
C' (-2,3)
C (x,y)
2
2
B' (-4,2)
C (3,2)
A' (-1,1)
A (1,1)
5
RULE FOR ROTATION BY 90 ABOUT THE ORIGIN RO ,90 ( x, y)  ( y, x)
4
Rotation of 180
B (2,4)
C (3,2)
2
When we rotate by
origin, we see the x
and y coordinates are
negated.
2
C (x,y)
A (1,1)
A' -(1,-1)
C' (-3,-2)
2
2
C' (-x,-y)
'B (-2-,4)
4
RULE FOR ROTATION BY 180 ABOUT THE ORIGIN RO ,180 ( x, y )  ( x,  y )
Rotation of 270
This is also a
rotation of - 90.
When we rotate by 270
that the x and y
coordinates are reversed
and the new y coordinate
is negated.
4
B (2,4)
2
C (x,y)
2
C (3,2)
A (1,1)
5
A' (1,-1)
B' (4,-2)
2
2
C' (y,-x)
C' (2,-3)
RULE FOR ROTATION BY 270 ABOUT THE ORIGIN RO ,270 ( x, y )  ( y,  x)
```