Warm Ups Start with point P (4, -6). State the coordinates...

07.05 + Coordinate Transformations Day 2 mt.notebook January 11, 2017

Which One Doesn't

Belong - Wednesday?

Warm Ups

a bc

d

Warm Ups

Start with point P (4, -6). State the coordinates of P' based on the following transformations:

(a) reflected over the line y = 3

(b) reflected over the x-axis

(c) reflected over the line y = x


Warm Ups





(4, 12)

Warm Ups





(4, 12)

(4, 6)


Warm Ups





(4, 12)

(4, 6)

(-6, 4)

Learning Objectives

• I can apply transformation rules on the coordinate plane.


Success Criteria

If you reflect a point over the x-axis and then the y-axis, to what transformation is that equivalent?

Is the result different if you reflect the point over the y-axis and then the x-axis?

Translations on the Coordinate Plane

Translations are denoted two different ways:

(x, y) (x + h, y + k)

vector <h, k>

https://www.youtube.com/watch?v=A05n32Bl0aY

https://www.youtube.com/watch?v=A05n32Bl0aY



Translate (6, 4) by the vector <-3, -5>.

Ex #1:

typo in packet


Translate (6, 4) by the vector <-3, -5>.

This also means:Translate (6, 4) using the rule (x - 3, y - 5).

Ex #1:

typo in packet


Translating Shapes Practice

Ex #2:

(a) Translate triangle ABC by the vector <3, -1>. Label the new coordinates of triangle A'B'C'.

(b) Does the translation preserve orientation?

(c) Is it an isometry?

AB

C


Ex #2:

(a) Translate triangle ABC by the vector <3, -1>. Label the new coordinates of triangle A'B'C'.

(b) Does the translation preserve orientation?

(c) Is it an isometry?

AB

C3 to the right, 1 down

A'B'

C'

yes

yes



Ex #3:

What vector maps the pre-image onto the post-image? Write your answer in the form <h, k>.

A

B

CA'

B'

C'


Ex #3:

What vector maps the pre-image onto the post-image? Write your answer in the form <h, k>.

A

B

CA'

B'

C'

7 to the right0 up/down

<7, 0>


(5, -2)

Rotations on the Coordinate Plane

Ex #4:

(a) Rotate the point (5, -2)180 degrees about the origin. Label the new coordinates.

(5, -2)

(5, -2)


Ex #4:


(5, -2)


(5, -2)


Ex #4:


Turn your paper upside down and plot (5, -2). This is a rotation of 180 degrees.

(-5, 2)

If you connect the pre-image and post-image, the segment should go through the origin.

(5, -2)


(5, -2)

(b) Rotate the point (5, -2) 90 degrees about the origin (counterclockwise) about the origin. Label the new coordinates.

(c) Rotate the point (5, -2)270 degrees (counterclockwise) about the origin. Label the new coordinates.

(2, 5)

(-2, -5)


Coordinate Plane Rules

What is the rule for rotations based on the angle of rotation?

180℉ (x, y) ( , )

(3, 2)



180℉ (x, y) ( , )(3, 2) (-3, -2)

(3, 2)

(-3, -2)post-image

pre-image




180℉ (x, y) ( , )(3, 2) (-3, -2)

-x -y

(3, 2)

(-3, -2)post-image

pre-image



180℉ (x, y) ( , )

90℉ (x, y) ( , )

270℉ (x, y) ( , )

(all counterclockwise)

-x -y

(3, 2)



Ex #5:

Rotate triangle ABC 270 degrees counterclockwise about the origin. Label the new coordinates of triangle A'B'C'.

AB

C


Ex #6:

What transformation is depicted here? Based on your answer, follow up with the following information.

• Translation: what vector?• Reflection: what line?• Rotation: what angle?

A

B

CA'

B'

C'


A

B

CA'

B'

C'

over the line y = -1


Ex #6:




Ex #7:



A

B

CA'

B'

C'


A

B

CA'

B'

C'90 degrees


Ex #7:



Success Criteria

Rate Your Understanding (0 - 5)

Ex #8: If you reflect a point over the x-axis and then the y-axis, to what transformation is that equivalent?



Success Criteria

Rate Your Understanding (0 - 5)

Ex #8: If you reflect a point over the x-axis and then the y-axis, to what transformation is that equivalent?


rotation of 180 degrees

no, the results are the same

Warm Ups Start with point P (4, -6). State the coordinates...

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