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 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 flipped 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 “mirror” line — always perpendicular bisector of the segment connecting a point and its image.

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.

How do you construct a line of reflection?

1. Connect a pre-image vertex to its image vertex.

2. Draw the perpendicular bisector of that segment.

3. That bisector is your line of reflection.

What are the types of reflections?

• Horizontal → flips side-to-side

• Vertical → flips up/down

Key reminder about reflections

Even if the vertices look different, the pre-image and image are congruent because distance and angle measures are preserved.

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)

Why is a reflection a basic rigid motion?

Because it keeps everything the same:

• Distances (lengths of sides) stay the same

• Angle measures stay the same

• Pre-image and image are congruent

What’s a basic rigid motion?

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

Does “length” mean the same as distance?

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

What is another word for a translation?

like moving a shape without changing it.

What’s the first step to do a translation on a graph?

Look at direction first — right/left, then up/down.

How do you find the image after a translation?

Add/subtract the translation numbers to the coordinates:

• Right → add x +

• Left → subtract x -

• Up → add y +

• Down → subtract y -

How do you reflect over the x-axis?

Keep x the same, flip the y: (x, y) → (x, -y)

How do you reflect over the y-axis?

Keep y the same, flip the x: (x, y) → (-x, y)

How do you reflect over the line y = x?

Swap x and y: (x, y) → (y, x)

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

Size and shape stay the same — only position changes.

Example Translation:**

Point (-2, 3), slide right 3 and up 2 → ?

(-2+3, 3+2) = (1, 5)

Example Reflection:**(2, -3) reflected over the x-axis → ?

(2, 3)

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 the line of reflection?

The “mirror” line — it always lies in the middle between the pre-image and image.

Reflection rules for special lines:

• y = x → swap coordinates: (x, y) → (y, x)

• y = -x → swap and change signs: (x, y) → (-y, -x)

• x = k → distance from x=k is same on opposite side

• y = k → distance from y=k is same on opposite side

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