What is a reflection?
A reflection is a mirror image of the original figure. It is the result of a
transformation of a figure over a line called the line of reflection.
*In a reflection, each point of the preimage and its image are the same
distance from the line of reflection.*
1
Take point (-2, 5) and reflect
it across the y-axis.
Take point (-2, 5) and reflect
it across the x-axis.
What do you notice about the coordinates of the image points?
2
When reflecting a point over the
x-axis, which coordinate remains
the same?
If point A is 2 units above the x-axis,
what will be the y-coordinate of the
reflected point?
If point B is three units above the x-axis,
what will be the y-coordinate of the
reflected point?
If point C is one unit below the x-axis,
what will be the y-coordinate of the
reflected point?
3
When reflecting a point over the
y-axis, which coordinate remains
the same?
If point K is two units to the right of
the y-axis, what will be the x-coordinate of
the reflected point?
If point L is five units to the right of
the y-axis, what will be the x-coordinate
of the reflected point?
If point M is four units to the left of
the y-axis, what will be the x-coordinate of
the reflected point?
4
Triange ABC has vertices
A(5, 2), B(1,3), and C(-1,1).
Graph the figure and its reflected image
over the x-axis.
Find the coordinates of the
vertices of the reflected image.
5
Whiteboards:
Quadrilateral KLMN has vertices
K(2, 3)
L(5, 1)
M(4, -2)
N(1, -1)
Graph the figure and its reflection over
the y-axis. Then find the
coordinates of the vertices of
the reflected image.
6
Whiteboards:
Triange PQR has vertices
P(1, 4)
Q(3, 7)
R(4, -1)
Graph the figure and its reflection over
the x-axis. Then find the
coordinates of the vertices of
the reflected image.
7
How can you determine the coordinates of a figure after a reflection over the x-axis?
How can you determine the coordinates of a figure after a reflection over the y-axis?
8
Your friend is finding the coordinates of the image of a
triangle with vertices A(1, 1), B(4, 1) and C(1, 5) after a
reflection over the x-axis. He says the new coordinates
are Al(-1, 1), Bl(-4, 1) and Cl(-1,5). Is he right? Why or why
not?
9
Try this:
Suppose you reflect a triangle in Quadrant I over the y-axis, then translate the
image 2 units left and 3 units down. Is there a single transformation that maps
the preimage onto the image?
Explain
10
What transformation occurred?
A(-2, 5)
A'(2, 5)
B(4, -9)
B'(4, 9)
What about this one?
C(3, -5)
C'(-3, 5)
11