Unit 1 Review

Tips for how this test is graded.

Answering Open Ended Questions

Unit 1 Part 1 Review

After doing C.U.B.E. double check to make sure that you answered EVERY part of EVERY question before moving on.

Read the DIRECTIONS

- Ask questions if you do not understand the directions and what you are supposed to do.

Be as SPECIFIC as you can.

- Eliminate vague words (it, they, did)

- Restate the problem instead of using it or they.

- tell the operation you did

EXPLAIN your thinking

- ALL steps must be listed that you did or thought

2 is the highest score for an open ended.

- Vocabulary must be used

- Answer must be circled and have label if needed

Reflection

Translations

Rotations

Moving from 1 spot (Pre-image) on the coordinate grid along the x and y axis to a new location (Image)

A Reflection is a mirrored image, or a pre-image flipped over a line of reflection (aka mirror line, line of symmetry, or center line)

Every point is the same distance from the central line !

... and ...

The reflection has the same size as the original image

3 Things that I must always know or tell about the rotation.

To turn in a circular direction about a fixed point.

1. Angle of Rotation:

How many degrees will the object be moving?

2. Center of Rotation:

What will I be turning around?

Example 2

Example 1

Tricks or Patterns for Reflecting over an Axis

3. Direction:

Will I be moving clockwise or counterclockwise?

If I rotate 90 degrees clockwise around (-1,1), what will my new coordinates be?

REFLECTING OVER THE X:

Examples

Rectangle is shown in the coordinate plane below. Rectangle (not shown) has coordinates V (-6 , 4), T (-6 , 0), and S (0 , 0).

Are ABCD and RVST congruent?

What transformation happened to make RVST congruent to ABCD?

Answer

Example:

X- Stays the same

Y- Changes

Translation Notation

There is no trick to rotating around a point

Don't forget to use your Geotool or ruler.

REFLECTING OVER THE Y:

Parallel lines and n (not shown) were each translated. Could lines t and u shown in the coordinate plane below be the image of lines and n after translation? Explain your reasoning.

No, lines t and u cannot be the images because parallel lines are still parallel after they are translated, and lines t and u are not parallel.

Part A What are the coordinates of the image of point C when line segment BC in the coordinate plane above is reflected about the x-axis?

Part B What are the coordinates of the image of point C when line segment BC in the coordinate plane above is reflected about the y-axis?

Part C What are the coordinates of the image of point C when line segment BC in the coordinate plane above is reflected about the origin?

(X , Y )

X+ = right Y+ = up

X- = left Y- = down

Tricks and Tips to Rotating ABOUT THE ORIGIN.

Y- Stays the same

X- Changes

Tricks or Patterns for Reflecting over Other Lines

Answer 1

What do you know about parallel lines?

90 & 270 degrees:

X & Y switch places and take sign of quadrant.

Are T and U parallel lines?

What is true about translated figures?

ABCD and RVST ARE congruent because when RVST is rotated 90 degrees counterclockwise the shapes will match up and become ABCD. Therefore, they are congruent.

REFLECTING OVER THE ORIGIN:

Answers

180 degrees:

X & Y stay the same; just change the signs to match the quadrant.

Answer

X & Y switch places and match sign of quadrant.

X= 2,6

Y= 4,2

Z= 0,4

When reflected from quadrant 1 over the X axis, point c should be in q 4. (+,-)

C (3,3) --> C' (3,-3)

REFLECTING OVER THE OTHER LINES:

When reflected from quadrant 1 over the Y axis, point c should be in q 2. (-,+)

C (3,3) --> C' (-3,3)

When reflected from quadrant 1 over the origin, point c should be in q 3. (-,-)

C (3,3) --> C' (-3,-3)

Don't forget to be the SAME distance from each point to the LOR. Fold the paper on the line of reflection(LOR) if you need to check your labels.

Sequence of Transformations

Dilations

Using multiple transformations (translations, reflections, rotations, and dilations) to get from a pre-image to a new image.

Enlarging (make bigger) or reducing (make smaller) to create images similar to their pre-images.

Example

Multiply by a Scale Factor

Example

When enlarging or reducing you have to multiply each number by a common scale factor.

Example 1

Quadrilaterals JKLM and WXYZ are shown in the coordinate plane below. Quadrilateral WXYZ is the image of quadrilateral JKLM under a transformation. Describe the following transformation.

8/4 = 2

Example 3

IMAGE: XY= 8

ORIGINAL: AB= 4

Quadrilateral ABCD shown in the coordinate plane below, is dilated with the center at the origin to form quadrilateral EFGH.

What is the scale factor of the dilation?

Explain your answer.

Example 2

6/3 = 2

IMAGE: YZ= 6

ORIGINAL: BC= 3

Describe a sequence (1+) of transformations

that can be used to show that triangle ABC

is congruent to triangle XYZ.

ABC is similar to XYZ by a scale factor of 2.

A transformation maps a preimage triangle to the image triangle shown in the coordinate plane below. If the preimage triangle is reflected over the x-axis to get the image triangle, what are the coordinates of the vertices of the preimage triangle?

Parallelogram EFGH is shown in the coordinate plane below.

Rotate EFGH 90 degrees clockwise about the origin and then translate it 4 units down.

Label the resultant image PQRS

Triangle is shown in the coordinate plane below. Triangle (not shown) is located in the coordinate plane with vertices at points X (6,0) Y (4,4) and Z(4,0) .

How can I get from XYZ to ABC?

How is triangle ABC congruent to triange XYZ?

notice it is not just multiplying the coordinates sometimes.

Answer 1

Answer 2

Notice that you are told JKLM (preimage) to WXYZ (image)

Lets compare the sides...

FD =

AB =

What do I need to multiply by to get from 4 to 6, from 9 to 6, from 12 to 8?

Image/

original

Lets compare the sides...

ZY = 2

ML = 3 = 2/3

GH =

CD =

8/12 = 2/3

WX = 8

JK =12

I had a dilation with a scale factor of..

2/3