TODAY IN GEOMETRY…

STATs for Ch.4 Test

Learning Target : 9.1-9.2 Given a pre-image, create an image by transformation by translation/slide or reflection

Independent Practice

AT: Ch.4 Test Corrections

HOW DID YOU “SHAPE” UP??Results for ALL of my Geometry classes:

GRADE NUMBER OF STUDENTS WHO TOOK THE CH.4 TEST (50 pts.)

1ST PERIOD 2ND PERIOD 4TH PERIOD 6TH PERIOD TOTAL

A 2 5 1 8 16B 7 6 5 5 23C 6 5 5 4 20D 4 2 3 2 11F 6 8 6 7 27

Avg 35.32 36.33 33.80 37.71 35.79

PRE-IMAGE: Starting figure of a transformation labeled as

IMAGE: Ending figure of a transformation labeled as

TRANSLATION/SLIDE: Moves every point of a figure the same distance in the same direction

𝐴𝐵

𝐶𝐷

𝐴 ′𝐵 ′

𝐶 ′𝐷 ′

𝐴 ′ ′𝐵 ′ ′

𝐶 ′ ′𝐷 ′ ′

Translated/slide 7 units right

Translated/slide 8 units down

x-coordinates change by adding 7

y-coordinates change by subtracting 8

TRANSFORMATION COORDINATE RULE EXAMPLE

Translation (shift)

Reflection across

Reflection across

Reflection across line

Reflection across line

counterclockwise rotation

rotation

counterclockwise rotation

(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)

PRACTICE: Graph . Translate the Pre-Image and record the image points.

𝐴𝐵

𝐶

𝐴 ′𝐵 ′

𝐶 ′

PRACTICE: Write a rule for the translation of the quadrilateral to quadrilateral .

How did the quadrilateral move?To the right 6 Down 6

Right/Up = ADDLeft/Down = SUBTRACT

Rule:

𝐴𝐵

𝐶 𝐷𝐴 ′𝐵 ′

𝐶 ′ 𝐷 ′

In Class Work #1:

Pg. 576: 3-14, 31

20 minutes then you will turn it in then we are moving on to

reflection.

TRANSFORMATION COORDINATE RULE EXAMPLE

Translation (shift)

Reflection across

Reflection across

Reflection across line

Reflection across line

counterclockwise rotation

rotation

counterclockwise rotation

(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)

REFLECTION across the x-axis:

𝐴𝐵

𝐶𝐷

Reflection across the x-axis so the x-axis is the mirror

5

5

𝐴 ′

𝐷′

𝐵′

𝐶 ′

Notice that all x-coordinates of the pre-image and image DOESN’T change but the y-coordinates change signs!RULE:

The distances from the mirror to each point is equal!

TRANSFORMATION COORDINATE RULE EXAMPLE

Translation (shift)

Reflection across

Reflection across

Reflection across line

Reflection across line

counterclockwise rotation

rotation

counterclockwise rotation

(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)

(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)

REFLECTION across the y-axis:

𝐴𝐵

𝐶𝐷

Reflection across the y-axis so the y-axis is the mirror

33𝐵′

𝐶 ′𝐷′

𝐴′

Notice that all y-coordinates of the pre-image and image DOESN’T change but the x-coordinates change signs!RULE:

The distances from the mirror to each point is equal!

TRANSFORMATION COORDINATE RULE EXAMPLE

Translation (shift)

Reflection across

Reflection across

Reflection across line

Reflection across line

counterclockwise rotation

rotation

counterclockwise rotation

(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)

(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)

(𝑦 ,𝑥) (−5 ,2) →(2 ,−5)

REFLECTION across line :

𝐴𝐵

𝐶𝐷

Reflection across the line

𝐵′𝐶 ′

𝐷′

𝐴′

Notice that the x and y coordinates switch values from pre-image to image.RULE:

TRANSFORMATION COORDINATE RULE EXAMPLE

Translation (shift)

Reflection across

Reflection across

Reflection across line

Reflection across line

counterclockwise rotation

rotation

counterclockwise rotation

(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)

(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)

(𝑦 ,𝑥) (−5 ,2) →(2 ,−5)

(− 𝑦 ,− 𝑥) (−4 ,−6) →(6 ,4)

REFLECTION across line :

𝐴𝐵

𝐶𝐷

Reflection across the line

𝐷′𝐴 ′

𝐵′

𝐶 ′

Notice that the x and y coordinates switch values from pre-image to image.RULE:

PRACTICE: Graph . Reflect the pre-image across the y-axis.

RULE FOR RELECTION ACROSS Y-AXIS:

𝐴𝐵

𝐶

𝐴 ′ 𝐵 ′

𝐶 ′

PRACTICE: Graph . Reflect the pre-image across the line .EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF REFLECTION

𝐴𝐵

𝐶

𝐴 ′ 𝐵 ′

𝐶 ′

𝑥=1

HOMEWORK #2:

Pg. 593: 3-6, 8-10, 27-29

If finished, work on other assignments:

HW #1: Pg. 576: 3-14, 31