Reflections worksheet featuring six geometric figures to be reflected across specified lines on coordinate grids.

Let’s solve each reflection problem one by one. We’ll find the new coordinates of each shape after reflecting it over the given line.

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Problem 1: Reflection across line y = -x

Original points (from graph):
Looking at the green L-shape in quadrant III:
- Bottom-left corner: (-3, -4)
- Top-left corner: (-3, -2)
- Bottom-right corner: (-1, -4)

Rule for reflection over y = -x:
Swap x and y, then change both signs → (x, y) becomes (-y, -x)

Apply to each point:

- (-3, -4) → (4, 3)
- (-3, -2) → (2, 3)
- (-1, -4) → (4, 1)

So reflected points: (4,3), (2,3), (4,1)

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Problem 2: Reflection across line y = x

Original triangle points (in quadrant II):
From graph:
- (-4, 2)
- (-2, 4)
- (0, 1)

Rule for reflection over y = x: Swap x and y → (x, y) becomes (y, x)

Apply:

- (-4, 2) → (2, -4)
- (-2, 4) → (4, -2)
- (0, 1) → (1, 0)

Reflected points: (2,-4), (4,-2), (1,0)

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Problem 3: Reflection across line x = 1

Original rectangle points (in quadrant I):
From graph:
- (1, 2)
- (1, 4)
- (4, 4)
- (4, 2)

Rule for reflection over vertical line x = a:
New x = 2a - old x; y stays same

Here, a = 1 → new x = 2(1) - x = 2 - x

Apply:

- (1,2) → (2-1, 2) = (1,2) ← on the line, doesn’t move
- (1,4) → (1,4) ← also on the line
- (4,4) → (2-4, 4) = (-2,4)
- (4,2) → (2-4, 2) = (-2,2)

Reflected points: (1,2), (1,4), (-2,4), (-2,2)

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Problem 4: Reflection across y-axis

Original triangle points (in quadrant I):
From graph:
- (0,1)
- (1,4)
- (5,1)

Rule for reflection over y-axis: Change sign of x → (x,y) → (-x,y)

Apply:

- (0,1) → (0,1) ← on axis
- (1,4) → (-1,4)
- (5,1) → (-5,1)

Reflected points: (0,1), (-1,4), (-5,1)

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Problem 5: Reflection across line y = 2

Original parallelogram points (in quadrant I):
From graph:
- (1,3)
- (2,5)
- (5,5)
- (4,3)

Rule for reflection over horizontal line y = b:
New y = 2b - old y; x stays same

Here, b = 2 → new y = 4 - y

Apply:

- (1,3) → (1, 4-3) = (1,1)
- (2,5) → (2, 4-5) = (2,-1)
- (5,5) → (5, 4-5) = (5,-1)
- (4,3) → (4, 4-3) = (4,1)

Reflected points: (1,1), (2,-1), (5,-1), (4,1)

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Problem 6: Reflection across x-axis

Original L-shape points (in quadrant IV):
From graph:
- (2,-7)
- (2,-5)
- (4,-5)
- (4,-3)
- (5,-3)
- (5,-5) — wait, let me check again from image.

Actually, looking carefully:

Points are:
- (2, -7)
- (2, -5)
- (4, -5)
- (4, -3)
- (5, -3)
- (5, -5) — but that might be duplicate? Let's list unique corners.

Better to trace the shape:

It looks like an L with these vertices:
Start at (2,-7) → up to (2,-5) → right to (4,-5) → up to (4,-3) → right to (5,-3) → down to (5,-5) → left to (4,-5)? Wait, maybe better to take outer corners.

Actually, standard way: pick all distinct vertex points.

From grid:

Bottom-left: (2, -7)
Top-left: (2, -5)
Then right to (4, -5)
Up to (4, -3)
Right to (5, -3)
Down to (5, -5) — but this is inside? Maybe it’s just 5 points?

Wait — perhaps simpler: the shape has these key points:

- (2, -7)
- (2, -5)
- (4, -5)
- (4, -3)
- (5, -3)
- (5, -5) — actually, if you connect them, (5,-5) connects back to (4,-5)? That would make a closed shape.

But for reflection, we can reflect each point.

Rule for reflection over x-axis: Change sign of y → (x,y) → (x, -y)

Apply:

- (2, -7) → (2, 7)
- (2, -5) → (2, 5)
- (4, -5) → (4, 5)
- (4, -3) → (4, 3)
- (5, -3) → (5, 3)
- (5, -5) → (5, 5)

Reflected points: (2,7), (2,5), (4,5), (4,3), (5,3), (5,5)

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Now, compiling final answers for each problem as coordinate lists.

Final Answer:

1) Reflected points across y = -x: (4,3), (2,3), (4,1)
2) Reflected points across y = x: (2,-4), (4,-2), (1,0)
3) Reflected points across x = 1: (1,2), (1,4), (-2,4), (-2,2)
4) Reflected points across y-axis: (0,1), (-1,4), (-5,1)
5) Reflected points across y = 2: (1,1), (2,-1), (5,-1), (4,1)
6) Reflected points across x-axis: (2,7), (2,5), (4,5), (4,3), (5,3), (5,5)