Translations on coordinates in a Cartesian plane.
rotations on coordinates in a Cartesian plane.
reflections on coordinates in a Cartesian plane.
Important Vocabulary
Make sure your child is familiar with the
A figure is a translation if it is moved without rotation.
Translation Vector
A
You can see that the translation did not move the figure far because the vector translation is small.
square translated on cartesian grid
We will try a different vector translation of (3,-9) on the same red square
The new coordinates are:
(-1,-6); (-1,-1); (-6,-6); (-6,-1).
Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.
single triangle on cartesian grid
Task: Translate ΔABC with a vector translation of (6,-2)
Steps:
Find the coordinates of Δ ABC.
Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.
Pl Transformation: Example 2
Work through the two reflection examples below.
Reflection Transformation: Example 1
The coordinates of LMNO are:
(-7,5); (0,5); (-2,1); (-5,1)
LMNO is reflected over the X-axis
making the coordinates of
L1M1N1O1:
(-7,-5); (0,-5); (-2,-1); (-5,-1)
Note how the x-coordinates remain the
same but the y-coordinates change to
their opposite integer (i.e. the sign changes).
This is always the case with reflections over the X-axis.
Reflection Transformation: Example 2
The coordinates of PQSR are:
(-8,-3); (-2,-3); (-2,-6); (-8,-6)
PQSR is reflected over the Y-axis making
the coordinates of
P1Q1S1R1: (8,-3); (2,-3); (2,-6); (8,-6)
Note how the y-coordinates remain the
same but the x-coordinates change to
their opposite integer (i.e. the sign changes).
This is always the case with reflections over the Y-axis.
Discuss with your child how, when reflecting a figure over the x-axis, the figure remains the same distance from the y-axis and the y-coordinate therefore does not change. Similarly, when reflecting a figure over the y-axis, the figure remains the same distance from the x-axis and the x-coordinate therefore does not change.
Transformations Worksheets
Click the links below and get your child to try the transformation worksheets that will allow for practice with questions based on what is shown above.
Transformations: Vector Translations
Transformations: Rotations and Reflections
Transformations: Calculating Coordinates
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