Understanding Geometric Transformations on the Cartesian Plane: Translation, Reflection, Rotation, and Dilation

Transformations
Math 10 Week
3
Flordelie A. Mendiola
Teacher III
UPPER BICUTAN NATIONAL HIGH SCHOOL

CONTENTS
Translations, Reflections
and Rotations
Points on the Cartesian
Plane
Subtopi
c 1
Subtopi
c 2

Lesson Objectives
1
2
3
4
Describe the position of points in the Cartesian
plane relative to its coordinates.
Describe how to translate, reflect, or rotate a given
figure on a Cartesian plane.
Evaluate whether a certain transformation is a
translation, reflection, or rotation
Design an artwork using translation, reflection,
rotation,
or any combination of the three

DAY 1: SHORT REVIEW
ACTIVITY 1: REMEMBER THE PLOT!
Plot each of the given points on the same
cartesian plane. Name the quadrant that point lies in.
A (1, 5)
B(3, 0)
C(-1, 3)
D(-4, -4)
E(2, -4)
F (0, 1)
G (0, 0)
Quadrant: _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
Quadrant: _____

Lesson Purpose
The concept of transformation of a
figure, whether in its size, position, or
orientation, can be expressed
mathematically.
The concepts of translation, reflection,
and rotation are bundantly manifested all
around us, especially in nature, the arts,
and design

Transformatio
n
Translation Reflection
• a change in any
form or
appearance.
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VOCABULARY
• the operation of
changing (as by
rotation or
mapping) one
configuration or
expression into
another in
accordance with a
mathematical rule
Rotation Dilation

Translation
• is a change
that moves all
points of a
figure (image)
the same
distance in the
same direction
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VOCABULARY

Reflection
• is a change
represented by
a flip of a
figure (image)
over a “mirror,”
which usually is
a line but may
also be a point,
or a plane
(which are
called lines of
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• is a change that
turns every point
of a preimage
through a
specified angle
and direction
about a fixed
point (called the
center of rotation).
Rotation
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Dilation
• is a change in
the size of a
figure that
requires a
center point
and a scale
factor.
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VOCABULARY

Sub-topic 1
Points on the
Cartesian
Plane

Angle Properties of Rectangles
Explicitation
Key Concepts
• Named after the French
mathematician
and philosopher René Descartes.

Explicitation
Key Concepts
• The main parts are the x- and y-
axes, and the origin.

Explicitation
Key Concepts
• An ordered pair (x, y) means a
location (a point) on the Cartesian
plane

Explicitation
Key Concepts
• The Cartesian plane is divided into
4 quadrants. Quadrants are
labeled in a counterclockwise
manner. Note the signs of the
coordinates of a point in each
quadrant.

WORKED EXAMPLES
ACTIVITY 1: REMEMBER THE PLOT!
Plot each of the given points on the same
cartesian plane. Name the quadrant that point lies in.
A (1, 5)
B(3, 0)
C(-1, 3)
D(-4, -4)
E(2, -4)
F (0, 1)
G (0, 0)

Activity 2: Label Me!
I. Label the parts of the
Cartesian plane below using
the boxes provided. Then,
identify the ordered pair for
each point.

Integratio
n
How can I use math concepts in art making?
Three Trees, Two Clouds
byJohn Beerman
The Cathedral
by Auguste Rodin
After the Mona Lisa 2
by Devorah Sperber

Activity 2: Label Me!
In each of the items below, the
blue figure is the preimage
(initial image) and the
green figure is the image
(transformed image). Describe
how the change was made.
Choose from the words
translation, rotation, reflection,
or dilation for the answer
(using the layman’s definition
of each of the words*).

Reflections
How much do you rate yourself about the
understanding transformation?
Fully
Understand
Confused No Master

Understanding Geometric Transformations on the Cartesian Plane: Translation, Reflection, Rotation, and Dilation