Translations on the
Coordinate Plane
Translations on the
Coordinate Plane
• In chess, there are rules governing how
many spaces and in what direction each
game piece can be moved
• The diagram below shows the legal moves
of the piece known as the knight
Translations on the
Coordinate Plane
• A translation (sometimes called a slide) is
the movement of a figure from one
position to another without turning it
• Every point on the original figure is moved
the same distance and in the same
direction(s)
Translations on the
Coordinate Plane
• The new points of the new figure are
referred to as “prime” (for example, point
A translated below becomes A’ or A prime)
• The new figure below is referred to as
triangle A’B’C’
Translations on the
Coordinate Plane
• If you think of movements in terms of
positive and negative, movements to the
right and up are positive, while movements
to the left and down are negative
• In the figure below, triangle ABC has been
translated (6, -4)
Translations on the
Coordinate Plane Checkpoint
• A positive number in the x-coordinate
position of an ordered pair (3, 4) means to
translate in which direction?
RIGHT
• A negative number in the x-coordinate
position of an ordered pair (-3, 4) means to
translate in which direction?
LEFT
Translations on the
Coordinate Plane Checkpoint
• A positive number in the y-coordinate
position of an ordered pair (3, 4) means to
translate in which direction?
UP
• A negative number in the y-coordinate
position of an ordered pair (-3, -4) means
to translate in which direction?
DOWN
Translations on the
Coordinate Plane
• There are two ways to think of how to translate
a figure. Consider the figure below
• Each vertex of the triangle has been moved 6
units to the right and 4 units down
• Hence, a translation of (6, -4)
Translations on the
Coordinate Plane
• Another way to translate a figure in the
direction described by an ordered pair is to
add the ordered pair to the coordinates of
each vertex of the figure
• In the example below, A(-2, 3) B(-2, 1) and
C (-5, 1) make up the original triangle
Translations on the
Coordinate Plane
• Translate triangle ABC by (6, -4)
A(-2, 3)
B(-2, 1)
C(-5, 1)
+(6, -4)
+(6, -4)
+(6, -4)
A’(4,-1)
B’(4,-3)
C’(1,-3)
Translations on the
Coordinate Plane Checkpoint
• Describe the translation below using an
ordered pair:
M’
A’
H’
T’
M
A
H
T
(-7, -3)
Translations on the
Coordinate Plane Checkpoint
• Give the vertices of square MATH after a
translation of (2, 2):
M
A
M’ (3, 6)
A’ (6, 6)
H
T
T’ (6, 3)
H’ (3, 3)
Translations on the
Coordinate Plane Checkpoint
• Show how to mathematically translate square
MATH (2, -7)
M
A
M’ (3, -3)
A’ (6, -3)
H
T
T’ (6, -6)
H’ (3, -6)
Homework: