Identify translation, rotation, and reflection of geometric shapes in this math worksheet.

Let’s go through each problem one by one. We’re looking at how a shape changes from the original (in the gray box) to the next shapes shown. The three types of changes are:

- Translation = sliding the shape without turning or flipping it.
- Rotation = turning the shape around a point (like spinning it).
- Reflection = flipping the shape over a line (like a mirror image).

We’ll compare each new shape to the original and decide which transformation happened.

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Problem 1:

Original: A cross-shaped figure with a dot in the top-left square.

First new shape: Same orientation, just moved right → Translation

Second new shape: Still same orientation, moved further right → Translation

Third new shape: Now the dot is on the bottom — that means it was flipped vertically → Reflection

Wait — let’s double-check. Actually, looking again:

The third shape has the dot on the bottom arm of the cross. That’s not a reflection — if you reflect the original over a vertical line, the dot would be on the top-right. If you reflect over horizontal, dot goes to bottom-left? Hmm.

Actually, let’s think differently. Maybe we should look at the position relative to the whole shape.

Original: Dot is on the top-left square of the cross.

Shape 3: Dot is on the bottom square of the cross. That suggests the whole shape was rotated 180 degrees? Or reflected?

Wait — better approach: Compare positions.

In translation, the shape doesn’t turn or flip — only moves.

In rotation, it turns.

In reflection, it flips like a mirror.

Looking at Problem 1:

- First arrow: shape moves right → Translation
- Second arrow: shape moves more right → Translation
- Third shape: now the dot is on the bottom — but the cross is still upright? No — actually, in the third shape, the cross is oriented the same way, but the dot is on the bottom square. That can’t happen by translation alone. So maybe it’s a reflection?

Wait — I think I made a mistake. Let me re-express.

Actually, looking at the worksheet layout:

Each problem shows the original shape in the gray box, then three other shapes to the right, and under each of those three, there’s a blank line to write “translation”, “rotation”, or “reflection”.

So for Problem 1:

Original: Cross with dot on top-left square.

Shape A (first to the right): Same as original, just shifted right → Translation

Shape B (second): Also same orientation, shifted further → Translation

Shape C (third): Now the dot is on the bottom square of the cross. But the cross itself hasn’t turned — it’s still pointing up/down/left/right the same way. How did the dot get to the bottom? Only if the whole shape was flipped vertically — so Reflection over horizontal axis.

But wait — in reflection, the entire shape flips. So if you flip the original over a horizontal line through the center, the top-left dot would go to bottom-left. But in Shape C, the dot is on the bottom-center? Wait no — let's visualize.

Actually, perhaps I need to count squares.

Maybe it’s easier to think: In translation, every part moves same direction/distance.

In rotation, the shape turns around a point.

In reflection, it mirrors.

For Problem 1, Shape C: The cross looks identical except the dot is now on the bottom square instead of top-left. That suggests the shape was rotated 90 degrees clockwise? Let’s see:

If you rotate the original 90° clockwise, the top-left square becomes top-right? Not matching.

Rotate 180°: top-left becomes bottom-right.

Still not matching.

Perhaps it’s a reflection over the vertical midline? Original dot on left side; after reflection, dot on right side — but in Shape C, dot is on bottom.

I think I’m overcomplicating.

Let me look at the example given at the top of the page.

In the example:

- Translation: shape slides right, dot stays in same relative position.
- Reflection: shape is mirrored over vertical dashed line — dot moves from right to left side.
- Rotation: shape turns 90° clockwise — dot moves from top-right to bottom-right.

Ah! So in rotation, the dot moves because the whole shape turns.

Back to Problem 1:

Original: dot on top-left square of cross.

Shape A: dot still on top-left, shape moved right → Translation

Shape B: same → Translation

Shape C: now dot is on the bottom square of the cross. That means the cross must have been rotated so that what was the top is now the bottom. Specifically, if you rotate 180°, the top-left square goes to bottom-right. But in Shape C, the dot is on the bottom-center? Wait, no — in the cross, the "bottom" square is directly below the center.

Actually, in the original, the dot is on the top arm of the cross. In Shape C, the dot is on the bottom arm. So if you flip the cross over a horizontal line, the top arm goes to bottom arm — that’s a reflection over horizontal axis.

Yes! So Shape C is a Reflection.

But let’s confirm with the example: in the reflection example, they used a vertical mirror line, and the dot moved from right to left. Here, if we use a horizontal mirror line, dot moves from top to bottom.

So for Problem 1:

- First shape: Translation
- Second shape: Translation
- Third shape: Reflection

But wait — the third shape might also be a rotation. If you rotate 180°, the top-left dot would end up on the bottom-right. But in the cross, the bottom-right isn't a square — the cross has arms: top, bottom, left, right, and center.

Original: dot on top square.

After 180° rotation: dot would be on bottom square — yes! Because rotating 180° swaps top and bottom, left and right.

So both reflection over horizontal and rotation by 180° would put the dot on the bottom square.

How to distinguish?

In reflection over horizontal, the left and right stay the same — so if there was something on the left, it stays on left.

In rotation 180°, left goes to right, right goes to left.

In our case, the cross is symmetric left-right, so we can’t tell from the shape alone. But the dot’s position: in original, dot is on top-left — but in the cross, the "top" square is centered, so "top-left" might mean the top square, which is above the center.

Actually, looking back at the image description — in Problem 1, the original has the dot in the top square of the cross (not top-left corner of the grid, but the top arm of the cross).

Similarly, in Shape C, the dot is in the bottom arm of the cross.

Since the cross is symmetric, rotating 180° or reflecting over horizontal both give the same result for the dot position.

But in terms of the transformation type, we need to see which one matches the movement.

Perhaps for this level, they consider any change where the shape is flipped as reflection, and turned as rotation.

But let’s look at Problem 2 for clue.

Problem 2:

Original: L-shape with dot on top-right square.

Shape A: L-shape turned so it’s facing down, dot on bottom-right → that’s a rotation (90° clockwise)

Shape B: L-shape facing left, dot on bottom-left → another rotation

Shape C: L-shape facing up, but dot on top-left — that would be reflection over vertical axis.

So for Problem 2:

- Shape A: Rotation
- Shape B: Rotation
- Shape C: Reflection

That makes sense.

Back to Problem 1:

If Shape C has the dot on the bottom, and the cross is otherwise the same, it could be either, but since the cross is symmetric, perhaps they intend it as rotation.

But let’s check the answer key logic from similar problems.

I recall that in such worksheets, when the shape is turned, it’s rotation; when flipped, it’s reflection.

In Problem 1, Shape C: the cross is not turned — it’s still oriented the same way (arms up, down, left, right), but the dot is on the bottom instead of top. That suggests the shape was flipped over a horizontal line — so Reflection.

Whereas if it were rotated, the arms would be in different directions.

For example, if you rotate the cross 90°, the top arm becomes the right arm, etc.

In Shape C of Problem 1, the cross still has arms in the same directions — up, down, left, right — so it hasn’t been rotated; it’s been reflected over horizontal axis.

Yes, that makes sense.

So for Problem 1:

- First: Translation
- Second: Translation
- Third: Reflection

Now Problem 2:

Original: L-shape with dot on top-right.

Shape A: L is now pointing down, dot on bottom-right → rotated 90° clockwise → Rotation

Shape B: L pointing left, dot on bottom-left → rotated another 90° → Rotation

Shape C: L pointing up, but dot on top-left → this is a mirror image of original — so Reflection over vertical axis.

Yes.

Problem 3:

Original: zigzag shape with dot on top-right.

Shape A: same shape, moved right → Translation

Shape B: same, moved further → Translation

Shape C: now the shape is flipped — the zigzag is mirrored, and dot is on bottom-right → Reflection

Because the shape is reversed left-right.

Problem 4:

Original: L-shape with dot on top-right.

Shape A: L pointing down, dot on bottom-right → Rotation 90° CW

Shape B: L pointing left, dot on bottom-left → Rotation another 90°

Shape C: L pointing right, but dot on bottom-right — wait, original was dot on top-right, after two rotations (180°), dot should be on bottom-left. But here it’s on bottom-right? Let’s see.

After 180° rotation, top-right goes to bottom-left.

But in Shape C, the L is pointing right, and dot is on bottom-right — that doesn’t match 180° rotation.

Perhaps it’s a reflection.

Original: L with short arm on top, long arm down, dot on top-right.

Shape C: L with short arm on bottom, long arm up, dot on bottom-right — that’s a reflection over horizontal axis.

Yes.

So:

- Shape A: Rotation
- Shape B: Rotation
- Shape C: Reflection

Problem 5:

Original: rectangle made of 6 squares, dot on top-right.

Shape A: same rectangle, moved right → Translation

Shape B: rectangle turned 90°, so now tall, dot on bottom-right → Rotation

Shape C: rectangle back to original orientation, but dot on bottom-right — that would be reflection over horizontal axis.

After rotation to vertical, then if you reflect over horizontal, dot goes from bottom-right to top-right? No.

Let’s track:

Original: wide rectangle, dot top-right.

Shape A: same, translated → Translation

Shape B: rotated 90° CW, so now tall rectangle, dot was top-right, after 90° CW, it becomes bottom-right → Rotation

Shape C: now wide rectangle again, but dot on bottom-right — compared to original, dot is on bottom instead of top, so reflection over horizontal axis.

Yes.

Problem 6:

Original: T-shape with dot on top-right.

Shape A: T-shape turned upside down, dot on bottom-right → Rotation 180°

Shape B: T-shape on its side, dot on bottom-left → Rotation another 90°? From upside down, rotate 90° CCW or CW.

From original to Shape A: 180° rotation.

From Shape A to Shape B: if you rotate 90° CW, the T would be pointing left, dot on bottom-left — yes.

Shape C: T-shape pointing right, dot on bottom-right — this is a reflection of the original over vertical axis? Original dot on top-right, after reflection over vertical, dot on top-left — not matching.

Shape C has dot on bottom-right, and T pointing right.

Compared to original, it’s like the T was flipped over horizontal axis — dot goes from top to bottom.

And the T is still pointing up? No, in Shape C, the T is pointing right? Let’s assume from context.

Perhaps for consistency:

- Shape A: Rotation (180°)
- Shape B: Rotation (another 90°, total 270°)
- Shape C: Reflection (over horizontal)

Problem 7:

Original: plus sign with dot on top-right.

Shape A: plus sign moved right, dot on bottom-right — wait, if it’s translated, dot should be on top-right. But here dot is on bottom-right, so not translation.

Shape A: the plus sign is the same orientation, but dot is on bottom-right — that suggests the shape was rotated or reflected.

If rotated 90° CW, top-right dot goes to bottom-right — yes!

So Shape A: Rotation

Shape B: plus sign, dot on top-left — from original, if rotated 180°, top-right goes to bottom-left; if reflected over vertical, top-right goes to top-left — so Reflection

Shape C: plus sign, dot on top-right — same as original, but moved — Translation

Let’s list:

Original: dot top-right

Shape A: dot bottom-right → Rotation 90° CW

Shape B: dot top-left → Reflection over vertical axis

Shape C: dot top-right, shape moved → Translation

Problem 8:

Original: rectangle 2x3, dot on top-right.

Shape A: same rectangle, moved right → Translation

Shape B: rectangle turned 90°, so tall, dot on bottom-right → Rotation

Shape C: rectangle back to wide, but dot on bottom-right — reflection over horizontal axis.

Now, compiling all answers:

Problem 1:
- Shape 1: Translation
- Shape 2: Translation
- Shape 3: Reflection

Problem 2:
- Shape 1: Rotation
- Shape 2: Rotation
- Shape 3: Reflection

Problem 3:
- Shape 1: Translation
- Shape 2: Translation
- Shape 3: Reflection

Problem 4:
- Shape 1: Rotation
- Shape 2: Rotation
- Shape 3: Reflection

Problem 5:
- Shape 1: Translation
- Shape 2: Rotation
- Shape 3: Reflection

Problem 6:
- Shape 1: Rotation
- Shape 2: Rotation
- Shape 3: Reflection

Problem 7:
- Shape 1: Rotation
- Shape 2: Reflection
- Shape 3: Translation

Problem 8:
- Shape 1: Translation
- Shape 2: Rotation
- Shape 3: Reflection

I think this is consistent.

Final Answer:

1) Translation, Translation, Reflection
2) Rotation, Rotation, Reflection
3) Translation, Translation, Reflection
4) Rotation, Rotation, Reflection
5) Translation, Rotation, Reflection
6) Rotation, Rotation, Reflection
7) Rotation, Reflection, Translation
8) Translation, Rotation, Reflection