REFLECTIONS & TRANSLATIONS
SECONDARY 1 MATH
E’
D’
A’
C’
B’
A
B
C
E D
Pre-Image
the original shape or object before any transformation has occurred
Image
the position of the new shape or object after a transformation has occurred
use an apostrophe to indicate that it has been moved, call new shape “prime”
list the new coordinates (x,y) in relation to the Origin (0,0)
A’
C’ B’
Reflection
a transformation in which every point in the pre-image appears at an equal
distance on the opposite side of a given line – the line of reflection– to form
an image
FLIP
distance to the line of reflection
must be perpendicular
Line of Reflection
the equation of a straight line which the pre-image is reflected across
can be horizontal, vertical, or diagonal
A
B
C
Graph each figure and its image under the given reflection then state the new vertices.
with vertices
in the x-axis.
A
C
B
B’
C’
A’
A’ (−5 ,−3)
B’ ( 2 , 0 )
C’ ( 1 ,−2)
Graph each figure and its image under the given reflection then state the new vertices.
with vertices
and
across the y- axis.
Q
P
R
S
Q’
P’
R’
S’
P’ ( 4 , 1 )
Q’ (−2 , 3 )
R’ (−2 ,−1)
S’ ( 4 ,−3)
has vertices
and
Graph and its image in the given line and state the new vertices.
J
L
K
J’
L’
K’
J’ (−8 , 3)
K’ (−6 , −1)
L’ (−2 , 1)
has vertices
and
Graph and its image in the given line and state the new vertices.
J
L
K
K’
L’
J’
J’ ( 0 , 1 )
K’ (−2 , 5 )
L’ (−6 , 3)
Graph each figure and its image under the given reflection then state the new vertices.
with vertices
about the line y = x
A
C
B
diagonal line of reflection
must travel diagonally
across squares to get to
the line
B’
C’
A’
A’ ( 3 ,−5)
B’ ( 0 , 2 )
C’ ( 2 , 1 )
Graph each figure and its image under the given reflection then state the new vertices.
with vertices
over the line y = x
Q
P
R
S
R’ Q’
S’ P’
P’ ( 1 , −4 )
Q’ ( 3 , 2 )
R’ (−1 , 2)
S’ (−3 ,−4)
Reflection Notation
for certain Lines of Reflection there are rules
Reflect across the x-axis:
Reflect about the y-axis:
Reflect across the line y = x :
y- coordinate is multiplied by −1
coordinates switch places
A
B
C
E D
Translation
a transformation in which every point in the pre-image is moved in
the same direction and distance to form an image
SLIDE
Translation Notation
A’
B’
C’
E’ D’
a = the distance the shape is moved sideways
positive = right negative = left
b = the distance the shape is moved vertically
positive = up negative = down
Describe the translation using translation notation.
4 units right
2 units down
P(2,4) → P’(6,2)
Q(1,2) → Q’(5,0)
x increased by 4
y decreased by 2
in each ordered pair
Graph a triangle with vertices
Sketch the image of the triangle after the translation
C
B
A
left 3 units
up 4 units
C’
B’
A’
A’ (−4 , 1)
B’ (−2 , 3 )
C’ (−4 , 4 )
Consider the translation that is defined by the translation notation
What is the image of ?
What is the pre-image of ?
What is the image of ?
X’(−1 , 10)
work backwards to find!
Y( 2 ,−12)
Z’(−5 , 10)