math vocabulary: unit 2: transformations

What is a reflection?

It’s like a mirror flip over a line — the image looks the same, just “flipped.”

Why is a reflection/ translation,/rotation called a basic rigid motion?

Because it doesn’t change size or shape the distance and angles stay the same.

What do you call the original figure?

The pre-image (or just the pre)

What do you call the new copy figure?

The image (look for primes: A’ B’ C’) can be any letter or look for different points that reflect the same area

What is the line of reflection?

the line that acts as a "mirror," flipping a figure to its "mirror image" on the opposite sidem it always lies in the middle between the pre-image and image.

a perpendicular bisector is

a line that cuts another line segment exactly in half and forms a perfect 90-degree angle with it. 

How do you know which points correspond?

Each vertex of the pre-image maps to one vertex of the image. Example: A → D, B → E, C → F or A’ B’ C’

What are the types of reflections?

• Horizontal → flips side-to-side

• Vertical → flips up/down

What kind of transformation makes a pre-image and image congruent? 

A rigid motion. It preserves distance and angle measures, so the shape stays the same size and form even if its position changes. 

Example of reflection

When your standing in front of a mirror you raise your right are and your reflection raise its left, you turn around and your reflection turns around

What are the four types of transformations, and which ones are basic rigid motions?

There are four transformations:

• Reflection ✅ (basic rigid motion)

• Slide / Translation ✅ (basic rigid motion)

• Rotation ✅ (basic rigid motion)

• Dilation ❌ (not a basic rigid motion)

What’s a basic rigid motion?

A transformation that preserves distance and angle measurements nothing gets bigger, smaller, or squished.

What is a nother word for distance

The length

What is another word for length

Distance

Does “length” mean the same as distance?

Yes! Length = distance = how long a side is.

What is another word for a translation?

Sliding like moving a shape without changing it.

If the x is positive then you move to the…

Right

Example of translation

A soccer ball is on the field it moves all around the field in many directions but it always stay the same size and shape

If the -x is negative you move to the…

Left

If the y is positive you move..

Up

If the -y is negative you move..

Down

What happens to the shape when you translate or reflect it?

Size and shape stay the same — only position changes.

How do you reflect over any line?

Graph the line first (the mirror), then count boxes so each point of the image is the same distance from the line as the original.

What is orientation?

The order of the vertices (clockwise or counterclockwise).

Do reflections preserve orientation?

❌ No! The vertices change order.

Do translations preserve orientation?

✅ Yes! The vertices stay in the same order.

What is point symmetry?

The figure looks the same upside down — every point has a matching point same distance from the center, opposite direction.

Quick tip to reflect over any line on graph paper:

1) Graph the line (mirror)

2) Count boxes from pre-image points to line

3) Place image points the same distance on the other side

What is a rotation?

A transformation that turns a figure around a fixed point (usually the origin).

What is a basic rigid motion?

A transformation that preserves distance (length) and angle measurements. Rotations are basic rigid motions.

What happens to a figure during a rotation?

The shape and size stay the same, but the figure turns around a point.

What does it mean when a rotation is “counterclockwise”?

It means the figure is turning to the left. This is the positive direction for rotation.

What does it mean when a rotation is “clockwise”?

It means the figure is turning to the right. This is the negative direction for rotation.

When you she this sign - ex:(-x,y) what does it mean

It means make opposite

Example of rotation

If your sitting in a cart on a faris wheel as the faris wheel is turning the cart you are riding in it taking you up down and a round

What is dilation

It’s a transformation that changes the size of a figure but keeps the same shape and angles. Bigger or smaller, but still looks the same! (The angle of the pre and image are congruent no matter how big or small they are in the difference size)

example of dilation

A cupcake.

• If you make a mini cupcake, it’s a reduction.

• If you make a giant cupcake, it’s an enlargem

What is a scale factor?

A number that tells how much bigger or smaller the figure gets.

• Less than 1 → smaller (reduction)

• Equal to 1 → same size

• Greater than 1 → bigger (enlargement)

How do you dilate a pre-image?

Multiply each side by the scale factor:

(scale factor) × (pre-image) = image

How do you find the scale factor if you know the pre-image and image?

Divide the image by the pre-image:

scale factor = image ÷ pre-image

Think of it as rip

Trick for graphing rotation

90 is turns the paper…

1 Time

Trick for graphing rotation

180 is turns the paper…

2 times

Trick for graphing rotation

270 turn the paper…

3 times

Trick for graphing rotation

360 turn the paper..

360 times

Uppercase, D represent?

Dilation

Lowercase r represents

Reflection

Uppercase R represents

Rotation

Upper case T represents

Translation

Scale factor is sometimes represented as the letter

r or k

Why is dilation not a basic ridged motion

Because it does not preserve length

The pre-image triangle in the image triangle in a dilation are….

Similar triangles

Similar triangles is

Similar figures

are shapes that have the same form, but can be different sizes. 

Try to remember that lowercase r reflection and uppercase R is rotation

• Big 'R' for Rotation (a big turn).

• Small 'r' for reflection (a small flip).

Translations (Sliding)

X in the rule is positive (+)

Slide right that many spaces → Add it to the pre-image x

Translations (Sliding)

X in the rule is negative (−)

Slide left that many spaces → Subtract it from the pre-image x

Translations (Sliding)

Y in the rule is positive (+)

Slide up that many spaces → Add it to the pre-image y

Translations (Sliding)

Y in the rule is negative (−)

Slide down that many spaces → Subtract it from the pre-image y

Rotations (Turning)

Rotate 90° (or −270°)

(x, y) → (−y, x)

Swap x and y, make y negative

Rotations (Turning)

Rotate 180° (or −180°)

(x, y) → (−x, −y)

Make both x and y negative

Rotations (Turning)

Rotate 270° (or −90°)

(x, y) → (y, −x)

Swap x and y, make x negative

Reflections (Flipping)

Reflect across X-axis

(x, y) → (x, −y)

Keep x, flip y

Reflections (Flipping)

Reflect across Y-axis

(x, y) → (−x, y)

Flip x, keep y

Reflections (Flipping)

Reflect across y = #

Keep x, change y

Reflections (Flipping)

Reflect across x = #

Keep y, change x

What is the center of dilation?

It’s the point that the figure is enlarged or reduced from.

👉 The pre-image stretches or shrinks away from (or toward) this point.

What does the symbol ~ mean?

~ means similar — the shapes have the same angles and proportional sides.

What is a scale drawing?

A figure that’s a bigger or smaller version of the original, made using a scale factor.

How do you draw arcs in a dilation?

The number of arcs depends on the scale factor.

What does “perimeter” mean?

The total distance around the shape — the sum of all side lengths.

How do you find the scale factor using side lengths?

Compare the image to the pre-image.

Formula:

(A’C’) / (AC) = (A’B’) / (AB) = (C’B’) / (CB)

If a figure got smaller after dilation, what does that mean about the scale factor?

The scale factor is less than 1, and the image is closer to the center of dilation.

If a figure got bigger after dilation, what does that mean about the scale factor?

The scale factor is greater than 1, and the image is farther from the center of dilation.

In the equation what does the y

In the equation mean

y = mx + b represent?

• output (the value on the y-axis)

In the equation what does the m

In the equation mean

y = mx + b represent?

• slope (how steep the line is)

In the equation what does the x

In the equation mean

y = mx + b represent?

• input (the value on the x-axis)

In the equation what does the b

In the equation mean

y = mx + b represent?

• y-intercept (where the line crosses the y-axis)

What happens when the center of dilation (COD) is on the line?

• The image line is the same exact line.

• It has the same slope and same y-intercept.

• The equation stays the same.
  ✅ Example: Pre-image: y = 2x − 3 → Image: y = 2x − 3

What happens when the center of dilation (COD) is not on the line?

• The image line is parallel to the pre-image line.

• It has the same slope but a different y-intercept.

• The y-intercept is multiplied by the scale factor.
  ✅ Example: Pre-image: y = 2x − 3 → Scale factor = 3 → Image: y = 2x − 9

How can you tell if the line will be the same or parallel?

1. Graph or imagine the line.

2. Check if the center of dilation point (COD) is on it.

3. If on, same line.
   If not on, same slope but new y-intercept (parallel).

Example — Line: y = 3x − 1, scale factor = 2, COD = (3, 8).

Since the COD is on the line, the image line stays the same:

Image equation: y = 3x − 1

Example — Line: 2y = −2x + 8, scale factor = 2, COD = (0, 0).

COD is not on the line, so multiply the y-intercept by the scale factor:

Pre-image: y = −x + 4 → Image: y = −x + 8

What happens when a figure is reflected over its line of symmetry?

It maps onto itself (the image and pre-image overlap).

What does perpendicular mean?

Two lines that meet at a 90° angle.

What does bisector mean?

It cuts something into two equal parts (the middle).

What is another way to describe a line of symmetry?

A perpendicular bisector.

Does every figure have a line of symmetry?

No, not all shapes do.

How do you find how many lines of symmetry a shape has?

The number of congruent sides equals the number of lines of symmetry.

What is the center of rotation?

The intersection of all the lines of symmetry.

How many rotations does a shape have?

The same number as its lines of symmetry.

How do you find the minimum angle of rotation?

Divide 360° by the number of sides (n).

Formula: 360 ÷ n

How do you find the degree measure of each rotation?

Start with the minimum rotation and keep adding it until you reach 360°.

Example: 120°, 240°, 360°.

When finding which letter maps onto which, which direction do you move?

Counterclockwise Ccw

Can you use rotation symmetry if not all sides are congruent?

No, the shape must be regular (all sides and angles congruent).

If shape has 3

Sides it is called

Triangle

If shape has 4

Sides it is called

Square

If shape has 5

Sides it is called

Pentagon

If shape has 6

Sides it is called

Hexagon

If shape has 7

Sides it is called

Heptagon

If shape has 8

Sides it is called

Octagon

If shape has 9

Sides it is called

Nonagon