Reflect and translate shapes - Geometry (Shape) Maths Worksheets ... - Free Printable

Since both ExplainAnswer and TeachTopic are false, and GeneratePractice is also false, we only need to provide the Final Answer — but with a critical rule:
> *Complete ALL reasoning and explanations BEFORE writing the Final Answer.*

However, the instruction says:
> “If an option is false, completely omit that section.”

But it also says:
> “IMPORTANT: Complete ALL reasoning and explanations BEFORE writing the Final Answer.”

This seems contradictory — but since the user has set all options to false, and the task is to “solve the problem accurately”, we must interpret this as:
→ We are expected to solve the problem (reflect shapes in both mirror lines), and then give the final answer — which for this type of worksheet would be the reflected shapes. But since we can’t draw, we describe them.

Also, note: The problem says “Reflect the following shapes in both mirror lines.” — meaning reflect over x-axis and y-axis? Or over both axes? Typically in such worksheets, “both mirror lines” means the x-axis and the y-axis.

Let’s go shape by shape.

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Shape 1 (top left):
Original shape: A 2x2 square missing the bottom-left corner → occupies (1,3), (2,3), (1,2), (2,2) — wait, let's check coordinates.

Looking at grid:
- Top row of shape: y=3, x=1 to 2 → squares at (1,3), (2,3)
- Bottom row: y=2, x=1 to 2 → but only (1,2) and (2,2)? Wait, no — actually, looking again:

Actually, from image:
It’s a 2x2 block starting at (1,2) to (2,3). So points:
(1,2), (2,2), (1,3), (2,3) — that’s a full 2x2 square? But in the image, it looks like it’s missing the bottom-left? Wait no — let me re-express.

Actually, in the first grid (top left), the shaded region is:
- From x=1 to x=2, y=2 to y=3 → that’s a 2x2 square? But visually, it appears as an L-shape? No — wait, I think I misread.

Looking carefully:
In top-left grid:
Shaded cells:
- (1,3), (2,3) — top row
- (1,2), (2,2) — bottom row? But that’s a full square. But the image shows a shape that looks like a rectangle with one cell missing? Actually, no — upon closer inspection, it’s a 2x2 square covering x=1,2 and y=2,3. But that doesn't match the visual — wait, perhaps it’s only three cells?

Wait — let’s list the shaded squares properly.

From the image (top left):
The gray shape covers:
- Column x=1: rows y=2 and y=3 → two cells
- Column x=2: only row y=3 → one cell
So it’s an L-shape: (1,2), (1,3), (2,3)

Yes — that makes sense. So original shape: {(1,2), (1,3), (2,3)}

Now, reflect over x-axis: (x,y) → (x, -y)
So:
(1,2) → (1,-2)
(1,3) → (1,-3)
(2,3) → (2,-3)

Reflect over y-axis: (x,y) → (-x, y)
So:
(1,2) → (-1,2)
(1,3) → (-1,3)
(2,3) → (-2,3)

But the problem says “in both mirror lines” — does that mean reflect over both axes separately? Or reflect over both to get a third image? Typically, it means do two reflections: one over x-axis, one over y-axis.

But the worksheet has 6 grids — 3 on left, 3 on right. Probably, for each original shape, you draw its reflection over x-axis in one grid, and over y-axis in another? But the layout is 3 rows, 2 columns — so likely, for each row, left grid is original, right grid is for one reflection? But there are 6 grids total.

Actually, looking at the image:
There are 6 separate grids. Each has a shape drawn. The instruction is: “Reflect the following shapes in both mirror lines.” — so probably, for each shape, you need to draw two reflections: one over x-axis, one over y-axis. But there are 6 grids — 3 originals and 3 blanks? No — all 6 have shapes.

Wait — actually, re-examining:
The first row: left grid has a shape, right grid has a different shape.
Second row: left has a cross-like shape, right has an L-shape.
Third row: left has a large L, right has a U-shape.

I think the intention is: for each of the 6 shapes, reflect it over both the x-axis and y-axis — but since there are only 6 grids, perhaps each grid is meant to be used for one reflection? That doesn’t make sense.

Alternative interpretation: Perhaps the "both mirror lines" means reflect over the x-axis AND over the y-axis, and you draw both reflections on the same grid? But the grids are empty except for the original shape.

Looking back at the image description:
Each grid has axes from -4 to 4. Some have shapes shaded. The instruction is to reflect the shapes in both mirror lines — likely meaning, for each shape, create two new images: one reflected over x-axis, one over y-axis.

But since there are 6 grids, and 6 shapes shown, perhaps each shape is to be reflected over both axes, and the student is to draw those reflections on the same grid or on separate grids? The worksheet doesn't specify.

Given the ambiguity, and since this is a standard type of problem, I will assume that for each given shape, we need to find its reflection over the x-axis and over the y-axis.

But the final answer should be the coordinates or description of the reflected shapes.

However, the problem is to "solve the problem accurately" — and since it's a drawing task, the answer might be expected as the coordinates of the reflected points.

But to be practical, let's handle each shape one by one.

Define "mirror lines" as the x-axis and y-axis.

For any point (x,y):
- Reflection over x-axis: (x, -y)
- Reflection over y-axis: (-x, y)

Now, let's list each shape's vertices or cells.

Shape A (top left grid):
Shaded cells: (1,2), (1,3), (2,3) [assuming integer coordinates for bottom-left corner of each cell]

Reflection over x-axis: (1,-2), (1,-3), (2,-3)
Reflection over y-axis: (-1,2), (-1,3), (-2,3)

Shape B (top right grid):
Shaded cells: Let's see — it's a T-shape or something? From image:
- Row y=-1: x=1,2,3 → (1,-1),(2,-1),(3,-1)
- Row y=-2: x=2 → (2,-2)
- Row y=-3: x=2 → (2,-3)? Wait, no — looking:
Actually, it's:
At y=-1: x=1,2,3 — three cells
At y=-2: x=2 — one cell
At y=-3: x=2 — one cell? But that would be a vertical line down from (2,-1) to (2,-3), plus horizontal at y=-1.

Standard T-shape: usually top bar and stem. Here, it seems:
Cells: (1,-1), (2,-1), (3,-1), (2,-2), (2,-3) — yes, a T pointing down.

So points: (1,-1), (2,-1), (3,-1), (2,-2), (2,-3)

Reflection over x-axis: (1,1), (2,1), (3,1), (2,2), (2,3)
Reflection over y-axis: (-1,-1), (-2,-1), (-3,-1), (-2,-2), (-2,-3)

Shape C (middle left grid):
Cross shape: center at (0,-1)? Let's see:
- Horizontal: y=-1, x=-1,0,1 → (-1,-1),(0,-1),(1,-1)
- Vertical: x=0, y=-1,-2 → (0,-1),(0,-2) — but (0,-1) is shared.
So cells: (-1,-1), (0,-1), (1,-1), (0,-2)

Reflection over x-axis: (-1,1), (0,1), (1,1), (0,2)
Reflection over y-axis: (1,-1), (0,-1), (-1,-1), (0,-2) — same as original since symmetric? Wait, no: reflection over y-axis of (-1,-1) is (1,-1), etc. But since the shape is symmetric about y-axis? Original has (-1,-1) and (1,-1), so yes, reflection over y-axis gives the same shape. But let's calculate:
(-1,-1) → (1,-1)
(0,-1) → (0,-1)
(1,-1) → (-1,-1)
(0,-2) → (0,-2)
So the set is {(1,-1), (0,-1), (-1,-1), (0,-2)} — which is the same as original. So reflection over y-axis is identical.

Reflection over x-axis: as above.

Shape D (middle right grid):
L-shape:
- y=-1: x=2,3 → (2,-1),(3,-1)
- y=-2: x=2,3 → (2,-2),(3,-2)? Wait, no — from image:
Actually, it's:
At y=-1: x=3 → (3,-1)
At y=-2: x=2,3 → (2,-2),(3,-2)
At y=-3: x=2 → (2,-3)? Let's see the grid.

Better: the shape covers:
- (3,-1)
- (2,-2), (3,-2)
- (2,-3)

So cells: (3,-1), (2,-2), (3,-2), (2,-3)

Reflection over x-axis: (3,1), (2,2), (3,2), (2,3)
Reflection over y-axis: (-3,-1), (-2,-2), (-3,-2), (-2,-3)

Shape E (bottom left grid):
Large L-shape:
- Top: y=3, x=2,3,4 → (2,3),(3,3),(4,3)
- Middle: y=2, x=3,4 → (3,2),(4,2)
- Bottom: y=1, x=4 → (4,1)

So cells: (2,3), (3,3), (4,3), (3,2), (4,2), (4,1)

Reflection over x-axis: (2,-3), (3,-3), (4,-3), (3,-2), (4,-2), (4,-1)
Reflection over y-axis: (-2,3), (-3,3), (-4,3), (-3,2), (-4,2), (-4,1)

Shape F (bottom right grid):
U-shape:
- Left: x=-2, y=-2,-3 → (-2,-2), (-2,-3)
- Bottom: y=-3, x=-1,0 → (-1,-3), (0,-3)
- Right: x=0, y=-2,-3 → (0,-2), (0,-3) — but (0,-3) shared.

Cells: (-2,-2), (-2,-3), (-1,-3), (0,-3), (0,-2)

Reflection over x-axis: (-2,2), (-2,3), (-1,3), (0,3), (0,2)
Reflection over y-axis: (2,-2), (2,-3), (1,-3), (0,-3), (0,-2)

Now, since the problem is to reflect in both mirror lines, and there are 6 shapes, the final answer should include all these reflections.

But how to present? Since it's a worksheet, perhaps the student is to draw them, but for text answer, we list the reflected coordinates.

Given the constraints, and since the user said "solve the problem accurately", I will provide the reflected coordinates for each shape over both axes.

But to keep it clean, I'll summarize.

Final Answer should be the set of reflected shapes.

However, the instruction says: "Provide only the final correct answer — this should come AFTER all explanations and reasoning."

And since we've done the reasoning, now we box the final answer.

But what is the final answer? It's not a single number. Perhaps for each shape, the reflections.

Maybe the problem expects the student to recognize that reflecting over both axes is equivalent to rotation by 180 degrees, but the problem says "in both mirror lines", which typically means two separate reflections.

Another interpretation: "reflect in both mirror lines" might mean reflect over the x-axis and then over the y-axis, which is the same as (x,y) -> (-x,-y).

But the problem says "in both mirror lines", plural, so likely two separate actions.

Given the worksheet has 6 grids, and 6 shapes, perhaps each grid is for one reflection, but that doesn't fit.

Perhaps for each shape, you draw its reflection over x-axis in one grid and over y-axis in another, but there are only 6 grids for 6 shapes, so maybe each shape is to be reflected over both axes on the same grid, but that would overlap.

I think the safest is to provide the coordinates for each reflection.

But to comply with the format, and since the final answer must be concise, perhaps list for each shape the two reflections.

Let me try to write it clearly.

For Shape 1 (top left):
- Over x-axis: cells at (1,-2), (1,-3), (2,-3)
- Over y-axis: cells at (-1,2), (-1,3), (-2,3)

For Shape 2 (top right):
- Over x-axis: (1,1), (2,1), (3,1), (2,2), (2,3)
- Over y-axis: (-1,-1), (-2,-1), (-3,-1), (-2,-2), (-2,-3)

For Shape 3 (middle left):
- Over x-axis: (-1,1), (0,1), (1,1), (0,2)
- Over y-axis: (1,-1), (0,-1), (-1,-1), (0,-2) [same as original due to symmetry]

For Shape 4 (middle right):
- Over x-axis: (3,1), (2,2), (3,2), (2,3)
- Over y-axis: (-3,-1), (-2,-2), (-3,-2), (-2,-3)

For Shape 5 (bottom left):
- Over x-axis: (2,-3), (3,-3), (4,-3), (3,-2), (4,-2), (4,-1)
- Over y-axis: (-2,3), (-3,3), (-4,3), (-3,2), (-4,2), (-4,1)

For Shape 6 (bottom right):
- Over x-axis: (-2,2), (-2,3), (-1,3), (0,3), (0,2)
- Over y-axis: (2,-2), (2,-3), (1,-3), (0,-3), (0,-2)

This is the complete solution.

Now, for the Final Answer, since it's a bit long, but necessary, I'll box it as a summary.

Perhaps the problem is to identify the reflections, and since it's a worksheet, the answer is the drawings, but for text, this is it.

I think this is as good as it gets.

So, final answer is the list above.

To make it neat, I'll write:

The reflections of each shape over the x-axis and y-axis are as follows:

Shape 1 (top left):
- x-axis reflection: (1,-2), (1,-3), (2,-3)
- y-axis reflection: (-1,2), (-1,3), (-2,3)

Shape 2 (top right):
- x-axis reflection: (1,1), (2,1), (3,1), (2,2), (2,3)
- y-axis reflection: (-1,-1), (-2,-1), (-3,-1), (-2,-2), (-2,-3)

Shape 3 (middle left):
- x-axis reflection: (-1,1), (0,1), (1,1), (0,2)
- y-axis reflection: (-1,-1), (0,-1), (1,-1), (0,-2) [note: same set as original]

Shape 4 (middle right):
- x-axis reflection: (3,1), (2,2), (3,2), (2,3)
- y-axis reflection: (-3,-1), (-2,-2), (-3,-2), (-2,-3)

Shape 5 (bottom left):
- x-axis reflection: (2,-3), (3,-3), (4,-3), (3,-2), (4,-2), (4,-1)
- y-axis reflection: (-2,3), (-3,3), (-4,3), (-3,2), (-4,2), (-4,1)

Shape 6 (bottom right):
- x-axis reflection: (-2,2), (-2,3), (-1,3), (0,3), (0,2)
- y-axis reflection: (2,-2), (2,-3), (1,-3), (0,-3), (0,-2)

This is the accurate solution.

Now, for the boxed final answer, since it's text, I'll present it as is.

But the instruction says "provide only the final correct answer", so perhaps just state that the reflections are as calculated.

I think for this context, the above is fine.

So, I'll box the entire thing, but that might be messy.

Perhaps the problem is to recognize that for each shape, the reflection over both axes means applying both transformations, but the answer is the set of points.

Another thought: in some contexts, "reflect in both mirror lines" might mean reflect over the line y=x or something, but that doesn't make sense with the grids.

I think my initial approach is correct.

So, final answer is the list.

To save space, I can say:

For each shape, the reflection over the x-axis is obtained by negating the y-coordinate, and over the y-axis by negating the x-coordinate. The specific coordinates are as listed above.

But for the box, I'll write the key points.

Since the user might expect a concise answer, and given that this is a worksheet, perhaps the answer is to be drawn, but for text, we describe.

I think I have to go with the detailed list.

So, here is the Final Answer:

\boxed{\begin{array}{c} \text{Shape 1:} \\ \text{x-axis: } (1,-2), (1,-3), (2,-3) \\ \text{y-axis: } (-1,2), (-1,3), (-2,3) \\ \\ \text{Shape 2:} \\ \text{x-axis: } (1,1), (2,1), (3,1), (2,2), (2,3) \\ \text{y-axis: } (-1,-1), (-2,-1), (-3,-1), (-2,-2), (-2,-3) \\ \\ \text{Shape 3:} \\ \text{x-axis: } (-1,1), (0,1), (1,1), (0,2) \\ \text{y-axis: } (-1,-1), (0,-1), (1,-1), (0,-2) \\ \\ \text{Shape 4:} \\ \text{x-axis: } (3,1), (2,2), (3,2), (2,3) \\ \text{y-axis: } (-3,-1), (-2,-2), (-3,-2), (-2,-3) \\ \\ \text{Shape 5:} \\ \text{x-axis: } (2,-3), (3,-3), (4,-3), (3,-2), (4,-2), (4,-1) \\ \text{y-axis: } (-2,3), (-3,3), (-4,3), (-3,2), (-4,2), (-4,1) \\ \\ \text{Shape 6:} \\ \text{x-axis: } (-2,2), (-2,3), (-1,3), (0,3), (0,2) \\ \text{y-axis: } (2,-2), (2,-3), (1,-3), (0,-3), (0,-2) \end{array}}

This is accurate and complete.