Geometry Worksheets | Transformations Worksheets - Free Printable

Let’s solve each reflection problem step by step.

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Problem 1: Reflection Across Line y = -x

Original shape has points at:
- (-4, -1)
- (-3, -1)
- (-3, -3)
- (-4, -3)

Rule for reflecting over y = -x:
(x, y) → (-y, -x)

Apply to each point:
- (-4, -1) → (1, 4)
- (-3, -1) → (1, 3)
- (-3, -3) → (3, 3)
- (-4, -3) → (3, 4)

New shape should have vertices at (1,4), (1,3), (3,3), (3,4) — a rectangle in the first quadrant.

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Problem 2: Reflection Across Line y = x

Original shape (triangle) has points:
- (-3, 2)
- (-1, 3)
- (-1, 1)

Rule for reflecting over y = x:
(x, y) → (y, x)

Apply:
- (-3, 2) → (2, -3)
- (-1, 3) → (3, -1)
- (-1, 1) → (1, -1)

New triangle should be in fourth quadrant with those points.

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Problem 3: Reflection Across the line x = 1

Original shape (L-shape) has points:
- (1, 2)
- (2, 2)
- (2, 1)
- (1, 1)
- (1, 0)
- (2, 0)

Wait — let’s list all corner points from the grid:

Looking at the green shape:
It goes from x=1 to x=3, y=0 to y=2.

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

Actually, better to trace the outline:

From the image, it looks like:
- Bottom-left: (1, 0)
- Then up to (1, 2)
- Right to (3, 2)
- Down to (3, 0)
- Left to (2, 0)
- Up to (2, 1)
- Left to (1, 1) — wait, that doesn’t close.

Actually, looking again — it’s an L-shape made of 3 squares:

Squares at:
- (1,0), (2,0), (1,1), (1,2), (2,2)

So corners:
- (1,0), (3,0), (3,2), (2,2), (2,1), (1,1), (1,2)

But simpler: reflect each point over x=1.

Rule: For vertical line x = a, reflection of (x,y) is (2a - x, y)

Here a = 1 → (x,y) → (2*1 - x, y) = (2 - x, y)

Apply:
- (1,0) → (1,0) [on line]
- (2,0) → (0,0)
- (3,0) → (-1,0)
- (3,2) → (-1,2)
- (2,2) → (0,2)
- (1,2) → (1,2)
- (1,1) → (1,1)
- (2,1) → (0,1)

So new shape will be mirrored to the left of x=1.

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Problem 4: Reflection Across the y-axis

Original triangle points:
- (0,0)
- (1,3)
- (5,0)

Rule: (x,y) → (-x, y)

Apply:
- (0,0) → (0,0)
- (1,3) → (-1,3)
- (5,0) → (-5,0)

New triangle in second quadrant.

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Problem 5: Reflection Across the line y = 2

Original parallelogram points:
- (1,2)
- (2,2)
- (3,3)
- (2,3)

Wait — let’s get exact points from grid:

From image:
- Bottom-left: (1,2)
- Bottom-right: (2,2)
- Top-right: (3,3)
- Top-left: (2,3)

Actually, it’s a parallelogram slanting right.

Points:
A(1,2), B(2,2), C(3,3), D(2,3)

Rule for horizontal line y = k: (x,y) → (x, 2k - y)

Here k=2 → (x,y) → (x, 4 - y)

Apply:
- (1,2) → (1,2) [on line]
- (2,2) → (2,2)
- (3,3) → (3,1)
- (2,3) → (2,1)

New shape below y=2.

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Problem 6: Reflection Across the x-axis

Original shape (steps) points:
- (2,-2)
- (3,-2)
- (3,-3)
- (4,-3)
- (4,-4)
- (5,-4)

Rule: (x,y) → (x, -y)

Apply:
- (2,-2) → (2,2)
- (3,-2) → (3,2)
- (3,-3) → (3,3)
- (4,-3) → (4,3)
- (4,-4) → (4,4)
- (5,-4) → (5,4)

New shape above x-axis, same steps but flipped up.

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Now, since the user didn’t specify which problem to solve, and all are shown, I’ll assume they want the answers for all 6 problems as coordinates of reflected shapes.

But the instruction says “provide the final correct answer” — so perhaps list all reflected vertex sets.

However, in many such worksheets, the student is expected to draw the reflection, not compute coordinates. But since we’re solving numerically, I’ll give the transformed points.

Final Answer:

1) Reflected points: (1,4), (1,3), (3,3), (3,4)
2) Reflected points: (2,-3), (3,-1), (1,-1)
3) Reflected points: (1,0), (0,0), (-1,0), (-1,2), (0,2), (1,2), (1,1), (0,1)
4) Reflected points: (0,0), (-1,3), (-5,0)
5) Reflected points: (1,2), (2,2), (3,1), (2,1)
6) Reflected points: (2,2), (3,2), (3,3), (4,3), (4,4), (5,4)

But to match typical worksheet expectations, maybe just state the rule applied and key points.

Since the task is to "solve the problem", and there are 6 problems, I'll provide the reflected coordinates for each.

Final Answer:

1) (1,4), (1,3), (3,3), (3,4)
2) (2,-3), (3,-1), (1,-1)
3) (1,0), (0,0), (-1,0), (-1,2), (0,2), (1,2)
4) (0,0), (-1,3), (-5,0)
5) (1,2), (2,2), (3,1), (2,1)
6) (2,2), (3,2), (3,3), (4,3), (4,4), (5,4)