1.7 Transformations in the Coordinate Plane
Geometry
Vocabulary
Transformation
A change in _______________, ________________, or
______________ of a figure.
Preimage
The original figure of a transformation.
Image
The resulting image after a transformation has occurred.
Reflection
A reflection, or _______, is a transformation across a line,
called the ___________________________. Each point
and it image are the same distance from the line of
reflection.
Rotation
A rotation, or __________, is a transformation about a
point P, called the ___________________________.
Each point and its image are the same distance from P.
Translation
A translation, or _____________, is a transformation in
which all points of a figure move the same distance in the
same direction.
Other Notes
In text, black is the preimage (original) and red is the image (after).
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1.7 Transformations in the Coordinate Plane
Geometry
A transformation maps every preimage to the image. Prime notation is used to denote the
image. Arrow notation is used to describe the transformation.
Mapping notation may also be used to describe a transformation.
Translation
(𝑥, 𝑦) → (𝑥 + 𝑎, 𝑦 + 𝑏)
Reflection
Over x-axis
(𝑥, 𝑦) → (𝑥, −𝑦)
Reflection
Over y-axis
(𝑥, 𝑦) → (−𝑥, 𝑦)
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1.7 Transformations in the Coordinate Plane
Rotation
180°
Geometry
(𝑥, 𝑦) → (−𝑥, −𝑦)
Examples
1. Identify the transformation. Then use arrow
notation to describe the transformation.
2. A figure has vertices at
𝐴(1, −1), 𝐵(2, 3), 𝑎𝑛𝑑 𝐶(4, −2). After a
transformation, the image of the figure has
vertices at 𝐴"(−1, 1), 𝐵′(−2, 3), 𝐶′(−4, −2).
Draw the preimage and image. Then identify
the transformation.
3. Find the coordinates for the image of ∆𝐴𝐵𝐶
if 𝐴(−4, 2), 𝐵(−3, 4), 𝑎𝑛𝑑 𝐶(−1, 1) after the
translation (𝑥, 𝑦) → (𝑥 + 2, 𝑦 − 3). Graph
the preimage and image. Label.
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