Translations in the Coordinate Plane

Students will be able to predict the results of
translations and draw translations on the
coordinate plane.
Transformation- maps one figure onto another
Translation- the motion of moving a figure
without turning it
Congruent Figures- same size and shape, and
the corresponding sides and angles have equal
Triangle TUV has vertices T(6,-3), U(-2,0),
and V(-1,2). Find the vertices of triangle
T’U’V’ after a translation of 3 units right
and 4 units down. Then graph the figure
an its translated image.
Students will be able to predict the results of a reflection and
graph reflections on a coordinate plane.
Scientists have determined that the
human eye uses symmetry to see. It is
possible to understand what you are
looking at even if you do not see all of
List all of the capital letters of the
alphabet that look exactly the same
when folded across a vertical line.
Line Symmetry: Figures that match exactly
when folded in half have line symmetry.
Line Symmetry: Each fold line is called a
line of symmetry.
Determine whether each figure has
line symmetry. If so, copy the figure
and draw all lines of symmetry.
Copy each figure. Draw the resulting
figure when each figure is lipped over
Does the size and shape
remain the same on
either side of the line of
What do you notice
about the distance from
the points to the line of
 Reflection- A mirror
produced by flipping a figure over
a line
 Line of Reflection- The line in
which an image is flipped to form
a reflection
 Image- the location or position of
a figure after a transformation
Count the units between a point and the
line of reflection.
For each point (vertex), plot a point an
equal distance away from the line of
reflection on the reflected side
Connect the vertices to form the reflected
Reflect the image over the y-axis
Reflect the figure using the x axis as
a line of reflection.
X (4, -4)
Y (-2,-3)
Z (2, -1)
What do you notice about the old coordinates
and the new coordinates? Is there a pattern?
Graph triangle FGH with vertices F
(1,-1) G (5, -3), H (2, -4). Graph the
image of triangle FGH after the
reflection over the y axis.
 Compare the new coordinates to the
old coordinates to find your rule.
The x values remain the same, the y
value changes sign
The y values remain the same, the x
value changes the sign.
Graph the figure with the given vertices. Then
graph the image of the figure after a reflection
over the x-axis. Then graph the image after it
has been translated up 2 units and right 3.
**Be sure to write the coordinates of the
image’s vertices.