M1.T2.L5. Transformations on Coordinate planes

TRANSFORMATIONS ON A

COORDINATE PLANE

TEKS: GEOM.3A DESCRIBE AND PERFORMTRANSFORMATIONS OF FIGURES IN A PLANE USING

COORDINATE NOTATION.

MODULE 1 | TOPIC 2 | LESSON 5 DAY 1

Learning Objective:

SWBAT describe and perform translations, reflections and rotations of figures using coordinate notation.

Demonstration of Learning:

Given a figure, students will correctly describe and perform translations, reflections, and rotations of figures using coordinate notation in at least 4 of 5 questions

VOCABULARY RECAP

Reflection

Translations

Rotations

A reflection is a rigid motion that “flips” a figure

across a line. A reflection as a function, Rℓ, takes as
its input, P, the location of a point with respect to
some line of reflection ℓ and outputs Rℓ (P), or the

opposite of the location of P with respect to the

line of reflection

A translation is a rigid motion that “slides” a

figure up, down, left, or right.

A rotation is a rigid motion that “spins” a figure
about a point. A rotation as a function maps its
input, a point P, to another location, f(P). This

movement to a new location is defined by a center

of rotation, E, and a rotation angle, t. For
this reason, a rotation function is written

as RE,t(P).

Example:

Example:

Example:

TRANSLATION

Original Point

Horizontal

Translation to

the Left

Horizontal

Translation to

the Right

Vertical

Translation

Up

Vertical

Translation

Down

( x, y)

(x - c, y)

(x + c, y)

(x, y + c)

(x, y - c )

Graph trapezoid ABCD by plotting the points A (3, 9),
B (3, 4), C (11, 4), and D (11, 10).

TRANSLATION

1. Translate trapezoid ABCD down 12 units. Label vertices: A',

B', C', D'.

2. Translate trapezoid ABCD to the left 15 units. Label vertices:

A", B", C", D".

TRANSLATION PRACTICE

Original Coordinates
(x,y)

Vertical Translation
Down
(x, y - c )

D

(-9,7)

E(-12,2)

F(-3,2)

G(0,7)

Open Ended

Is the rule in translating a parallelogram different from the rule in translating a trapezoid? Explain your reasoning.

Open Ended

How do you know which coordinate changes during the transformation?

Open Ended

How do you know which coordinate does not change during the transformation?

Categorize

Options (4)

(-9,-7)

(-12,-12)

(-3,-12)

(0.-7)

Image DEFG has the following vertex coordinates: D (-9,7), E (-12,2), F (-3,2), G (0,7).

Determine the vertex coordinate of image D'E' F'G', if image DEFG is translated 8 units to the right.

D"

E"

F"

G"

Multiple Choice

True or False:

" A translation will add or subtract constant values from the 𝑥 - and 𝑦 -coordinates."

• True

• False

REFLECTION RULES

1. Graph point J at (5, 7) on the

coordinate plane shown.

Open Ended

What difference do you notice when reflecting a point across the x-axis versus reflecting a point across the y-axis?

Categorize

Options (4)

(-9,-7)

(-12,-2)

(-3,-2)

(0,-7)

The vertices of parallelogram DEFG are D (–9, 7), E (–12, 2), F (–3, 2), and G (0, 7).

Determine the vertex coordinates of image D’E’F’G’ if parallelogram DEFG is reflected over the x-axis.

D'

E'

F'

G'

Categorize

Options (4)

(9,7)

(12,2)

(3,2)

(0,7)

The vertices of parallelogram DEFG are D (–9, 7), E (–12, 2), F (–3, 2), and G (0, 7).

Determine the vertex coordinates of image D’’E’’F’’G’’ if parallelogram DEFG is reflected over the y-axis.

D"

E"

F"

G"

ROTATION RULES

Categorize

Options (4)

(x,y)

(-y,x)

(-x,-y)

(y,-x)

If you are given coordinates (x,y), what are the coordinates if the point is rotated $$90\degree$$ , $$180\degree$$ , $$270\degree$$ , $$360\degree$$ ?

90

180

270

360

Multiple Choice

What quadrant will figure A be when rotated 180?

• I

• II

• III

• IV

ROTATION RULES

Original

(x,y)

(5,7)

90°

(-y,x)

180°

(-x,-y)

270°

(y,-x)

360°

(x,y)

Graphing

First, graph point Q at (5, 7).

Then, rotate counterclockwise and graph point Q', Q", and Q"', at $$90\degree$$ , $$180\degree$$ , $$270\degree$$ .

ROTATION PRACTICE

Graph trapezoid ABCD by plotting the points A (–12, 9), B (–12, 4),

C (–4, 4), and D (–4, 10). Then rotate trapezoid ABCD 90°, 180°, 270°, 360°.

Original
Coordinates

90
(-y, x)

180
(-x, -y)

270
(y, -x)

360
(x, y)

A (-12,9)

B (-12,4)

C (-4,4)

D (-4, 10)

Graphing

Rotate the triangle $$180\degree$$ counterclockwise and graph point B' in the correct quadrant.

Multiple Choice

Which figure represents a $$270\degree$$ counterclockwise rotation of $$\Delta B$$ ?

• A

• D

• C

D.O.L Time !!!