In the diagram above,
corresponding points on the
two figures are related.
Suppose P is any point on the
original figure and P’ is the
corresponding point on the
image figure.
We say: P maps onto P’
We write: P
P’
We often use a coordinate grid when we work with
transformations. We use a mapping rule to describe
how points and their images are related.
A mapping rule tells you what to do to the coordinates
of any point on the figure to determine the
coordinates of tits image.
Example of Mapping rule:
(x, y)
(x + 5, y - 2)
It tells you to add 5 to the x-coordinate and to subtract 2 from the
y-coordinate.
Reflections in the
Reflections in the line
YOU NEED TO MEMORIZE THESE RULES!!!
The image is congruent to the
original figure.
The orientation of the image is
reversed. That is, if triangle ABC
is read clockwise, then triangle
A’B’C’ is read counterclockwise.
Line segments that join matching
points are parallel. They are
perpendicular to the reflection
line and bisected by the reflection
line.
A triangle with vertices A’(-5,4), B’(-2,1), and C’(-6,-3) is the image of
triangle ABC under a reflection in the y-axis.
a) Draw a diagram to show the image triangle A’B’C’ and the original
triangle ABC.
b) Determine the coordinates of the vertices of triangle ABC.
a) On a coordinate grid draw triangle
A’B’C’. The original triangle ABC was
reflected in the y-axis to become
triangle A’B’C’.
Hence, we can reflect triangle A’B’C’ in
the y-axis to return to the original
triangle.
Since A’ is 5 units to the left of the y-axis,
A must be 5 units to the right of the yaxis.
Similarly, B is 2 units to the right of the yaxis, and C is 6 units to the right of the
y-axis.
b) The coordinates of the vertices of
triangle ABC are A(5,4), B(2,1), and
C(6,-3).
Combining Transformations: We can
use mapping rules to combine two reflections,
or to combine a reflection with a translation.
A polygon has vertices A(1,3), B(3,3), C(3,1), D(5,1), and
E(5,5).
a) Graph the polygon and its image, polygon A’B’C’D’E’,
under the translation (x,y)
(x+4,y+5)
b) On the same grid, graph the image of polygon
A’B’C’D’E’ under the reflection (x,y)
(-x,y)
a) Draw polygon ABCDE on a coordinate grid.
To apply the mapping rule (x,y)
(x+4,y+5),
we add up 4 to the x-coordinate and add 5
to the y-coordinate of each vertex of
polygon ABCDE.
This moves it 4 units right and 5 units up to
become polygon A’B’C’D’E’.
b) To apply the mapping rule (x,y)
(-x,y) to
the image, we multiply each x-coordinate by
-1 and keep the y-coordinate the same.
This reflects the image in the y-axis to become
polygon A”B”C”D”E”.
The coordinates of its vertices are A”(-4,8),B”(6,8),C”(-6,6),D”(-8,6), and E”(-8,10)
Class Work
• Copy Notes to Lesson 29
• Complete Lesson 29 worksheet