Space and Shape UnitGeometry

Grade 9 Math

Mapping RulesE1

Interpret, represent and apply mapping notation for transformations on the

coordinate plane

Things to review for this lesson:1. Watch this video and fill in a definition for each of

the terms (2-4)1. https://www.youtube.com/watch?

v=r3lN_BADmPQ

2. Translations 3. Reflection 4. Rotation5. Dilatation

What is a mapping rule?

A mapping rule is an algebraic expression that describes a change __________

Instead of verbal instructions, is numerical instructions

The instructions tell __________ (Moved? Reflected? Size?)

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: B: C:

A

BC

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: B: C:

Now, take point A and move it right 5 spaces and down 3. Label the new point A`

A

BC

A`

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: (-6, 7) B: (-4, 2) C: (-8, 2)

B would move in a similar way. If:B B`Then:(-4, 2) (____, _____)And C C`, then (-8, 2) (____, _____)

A

BC

A`

B`C`

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: (-6, 7) B: (-4, 2) C: (-8, 2)

B would move in a similar way. If:B B`Then:(-4, 2) )And C C`, then (-8, 2)

A

BC

A`

B`C`

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: B: C:

How could we determine the new coordinates (B` and C`) without plotting them on the grid?

A

BC

A`

B`C`

Activity #1

To make a mapping rule… What are the coordinates for Triangle ABC?A: B: C:

If we can say “I added 5 to x and subtracted 3 from y” we can also do show that with numbers.

Mapping rule:__________

A

BC

A`

B`C`

Break it down…

Mapping rules show the changes to x and y

(x, y) (x + 2, y +3)

Values of x and y

“are changed by…”

Change affecting y

Change affecting x

Activity #2

In your groups take this shape (pre-image) and translate it to a new spot on the grid.

Exchange images with another group.

Make the mapping rule for the other group’s image.

Trade back and compare

A

C

B

D

Activity #3

Complete the table of mapping coordinated to show change

Pre-Image Mapping rule New Coord’ates

(3, -2) (x,y) (x + 2, y + 3)

(0,6) ( -3,4)(x,y) (x - 2, y + 1) (8, 5)

(x,y) (-y, x) (2, 5)(-4, 1) (x,y) (3x, 3y)

Mapping Rule With Translation

x and y are both changed by addition and/or subtraction

They do not need to be changed the same amount

Pra

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e Q

uestio

n

Questio

n #

1

On a grid, create triangle RST with vertices R(-4, 4) S(-6, 2) T(-3, 2).

Translate triangle RST 4 spaces left. This is R`S`T`

1. What are the new coordinates of this triangle?

2. Compare the vertices of the original triangle. What is the mapping rule?

Translate R`S`T` 5 spaces down. This is R``S``T``

3. Explain why (x, y) (x-4, y-5) would describe the relation between the final position of the triangle (R``S``T``) and the original.

4. Without graphing, what would be the coordinates of R```S```T``` if the mapping rule was (x, y) (x+7, y-3)?