Transformations on a Coordinate Planedelaredemath2.weebly.com/uploads/2/9/7/4/29741177/...Guided/Independent Practice/Assessment Coordinate Grid Logic Color Classroom Posters for Reflection,

Transformations on a Coordinate Plane

Translation

ReflectionReflection

Translation

Rotation

Rotation

Written by Jena Phillips Caught in the Middle

Copyright ©2012

CCSS 8.G.2, 8.G.3, 8.G.4

http://mrsphillipsiscaughtinthemiddle.blogspot.com

http://mrsphillipsiscaughtinthemiddle.blogspot.com

Table of Contents

ReflectionStudent Notes

Guided/Independent Practice

TranslationStudent Notes


RotationStudent Notes


Dilation Student Notes


ExtrasCreate your own Transformation

Blank Grids

Multiple TransformationsGuided/Independent Practice/Assessment

Coordinate Grid Logic

Color Classroom Posters for Reflection, Translation, Rotation, Dilation

Reflection

x

y

Either single points or entire shapes can be flipped, or reflected, over a line. Sometimes the x and y axes are used as lines of reflection. Sometimes, the lines must be drawn in to solve the reflection. For example, if the line of reflection is at x = 2, a vertical line would be drawn at +2 and the reflection would take place across that line.

To reflect a shape across the x-axis, take the opposite y value of each point.

(3,3)

(3,-3)

© 2012 Jena Phillips

y

x

y To reflect a shape across the y-axis, take the opposite x value of each point.

(3,3)(-3,3)

x

line of reflection

There isn’t a rule for lines of reflection that are not the axes. The reflected shape must be as far from the reflection line as the original shape.


Reflection Practice

1. Label the x and y axes.

2.Label each of the points.

3. Reflect the shape across the x-axis.

4. Find the area of the shape.

5. Name the specific shape.

1.

2.

















3.

4.




3. Reflect the shape across the y-axis.






4. Find the sum of the interior angles.


5.

6.










4. Find the area of the shape. (Hint: Find the area of the rectangle that surrounds the triangle, then subtract the smaller triangles.)


7.

8.




3. Reflect the shape across the line of reflection.



9.



3. Reflect the shape across the line of reflection.



10.


TranslationA translation moves a pre-image point by point to slide the figure into a new location. The shape at the new location is called the image, and is noted with the ‘ symbol called prime. An original triangle ABC would be called A’B’C’ after the movement happens. The prime symbol helps to avoid confusion as to which is the original figure and which is the new one.

y

x

Translate this regular trapezoid 7 right, and 5 down.

pre-image

image

A B

CD

A’ B’

C’D’



2.Label each of the points in the pre-image with a letter. (Remember to move around the shape in alphabetical order.)

3. Translate the shape right 6, down 2.

4. Mark the image with the same letters, but use the prime symbol.



3. Translate the shape left 4, down 6.


Translation Practice

1.

2.




3. Translate the shape right 2, up 2.






3.

4.










5.

6.








3. Translate the shape left 4, up 2.


7.

8.




3. Translate the shape right 6, down 2.




3. Translate the shape left 6, up 5.


9.

10.


RotationThe rotation, or turn, is the most difficult of the transformations. When performing a rotation on a coordinate plane, it is usually called “about the origin.” This means that the point (0,0) is the center point of the rotation. Directional words like clockwise and counterclockwise are also used. Unlike the reflection and translation, the rotation isn’t a movement that is easily visualized. The rule for the rotation is also more difficult and can be confusing.

(2,3)(-3,2)

When rotating counterclockwise, there are two steps to finding the

new point.

1. Reverse the (x,y) numbers of a given point.

2.Take the opposite of the x number.

y


When rotating clockwise, follow similar steps to finding the new

point.

1. Reverse the (x,y) numbers of a given point.

2.Take the opposite of the y number.

(4,2)

(2, -4)

x

y

Rotating a figure 90°, puts it into the adjacent quadrant.

Rotating a figure 180°, puts it into the opposite quadrant. (To rotate 180°, complete the rotation twice.)


1.

2.

Rotation Practice


2. Label each of the points.

3. Rotate the figure 90° counterclockwise.

4. Shade in the image, but leave the pre-image unshaded.



3. Rotate the figure 90° clockwise.



4.









3.


5.

6.










7.

8.










9.

10.










DilationA dilation takes a shape on the coordinate plane and enlarges it, just as an eye doctor makes your pupils larger with dilation drops. To complete a dilation in math, we work with scale factors. A scale factor makes sure that as a shape is enlarged, it is done so proportionally. To complete a shape’s dilation, we change each individual point by multiplying the x and y values by the scale factor.

pre-image

The Scale Factor is 2.

(1,0) (3,0)

(3,2)(1,2)In a dilation, multiply each of the numbers of the coordinate points in the pre-image by the scale factor.

y

x


One point in the pre-image is (1,0). To use the scale factor of 2, multiply 1 x 2 to create the new image’s x value, and multiply 0 x 2 to create the

new image’s y value.

new image

The scale factor makes sure that both the height and the length has been multiplied by 2.

( 1,0) (2,0)(3,0) (6,0)(1,2) (2,4)(3,2) (6,4)

Multiply by the scale factor of 2.

y

x


1.

2.


2.Dilate the figure. The scale factor is 2.





Dilation Practice


4.

3.


2.Dilate the figure. The scale factor is 1/2. (Hint: the fraction will make the new image smaller.)



2.Dilate the figure. The scale factor is 1/4. (Hint: the fraction will make the new image smaller.)


Dilations that use a fraction as a scale factor are known as reductions.





5.


6.





7.





Create your own transformation for someone else to solve.

1. Give the pre-image.2.State what type of transformation you want your partner to perform

with any specific details that are needed.


Blank

gridsMake your own to use in class, in a center, or laminate them, put them on a ring and use as “Now that I’m Done” activity!


Multiple Transformations

1.Label the axes. 2.Create the pre-image at (0,2), (3,2),

(0,0), and (3,0).

3. Label the points A, B, C, D.

4.Translate the pre-image left 3 and down 3.

5.Shade the new image with colored pencil.

6. Rotate your shaded image 90° counterclock wise.

7. Label your final image points as A’B’C’D’.

8. In which quadrant is your final figure? ______________________________

Use all you have learned to solve the following problems about transformations on the coordinate plane.

1.


1.Label the axes. 2.Create the pre-image at (-2,-2), (-2,0), and (-5,-1).

3. Label the points X, Y, Z.

4.Reflect the image across the y axis.


6. Translate the new image left 3 and up 5.

7. Label your final image points as X’Y’Z’.

8. What is the area of the triangle? ______________________________

2.


1.Label the axes. 2.Create the pre-image at (1,2), (2,2), (1,1) and

(2,1).

3. Label the points L,M,N,P.

4.Dilate the image by a scale factor of 2.


6. Reflect the new image across the x axis.

7. Label your final image points as L’M’N’P’.

8. How much larger is the area of the dilated image than the pre-image? _____________________?

3.



Sam was playing a game on a coordinate grid using square pieces. He had to place a piece so that one of the vertices was located at (-3,6). If the area of his square was 16 square units and the piece was found entirely in the second quadrant, what are the coordinates of the other three vertices?



Anne was burying treasure in her backyard. In order to remember where her trunk was located, she drew a map on the coordinate plane. Using the origin as the location of her house, Anne slid the chest four paces north until she came to the location of a large elm tree. She then turned west and drug it another three paces before running into a muddy patch. She turns north once again for three paces and finds a perfect place to begin digging. When drawing the rectangular chest on her map, she was careful to draw the area of four square units. She also notices that the location was in both the first and second quadrants, what are the coordinates of her treasure chest?


Joey has a box where the length is three times the size of the width. When it is reflected across the x and y axis, it fits completely within each of the quadrants. Give possible coordinates for the beginning location of the box.



Susie was building a fence around her new vegetable garden. She put two posts of the fence at (-1, 0) and (-5,4). If the garden was a parallelogram with an area of 36 square units, where should the other two fence posts be located?



Over the x axis: Take the opposite y

value.

Over the y axis: Take the opposite x

value.

Reflection(Flip)

Translation(Slide)

Move the pre-image point by point to the new location.

This creates the new image.

Rotation

To rotate 90° counterclockwise about

the origin:

°Reverse the (x,y) values.

°Take the opposite of the x number.

(Turn)

Dilation(enlarge)

Multiply the (x,y) points by a scale factor to create

new points for the new image.

Using a scale factor less than 1, creates a smaller

version of the original, or a reduction.

Thanks for your purchase!

I hope that you find these activities helpful in your classroom. If you

have enjoyed your download, please consider following my TpT site and

blog, Caught in the Middle.

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Documents

Transformations on a Coordinate Planedelaredemath2.weebly.com/uploads/2/9/7/4/29741177/...Guided/Independent Practice/Assessment Coordinate Grid Logic Color Classroom Posters for Reflection,