Reflection Worksheet | PDF | Geometry | Space - Free Printable

Since I can't view or access images directly, I’ll help you solve the reflection problems based on your description of the image. However, since the image contains six separate reflection tasks with figures on coordinate grids, I will walk you through how to solve each type of reflection, and then guide you through solving them step-by-step based on typical setups like these.

Let’s go through each problem one by one, explaining how to reflect a figure across a given line, and give you instructions for graphing the image.

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🔷 General Rule: Reflections in the Coordinate Plane

Here are the rules for reflections:

| Reflection Across | Rule (x, y) → |
|-------------------|----------------|
| x-axis | (x, -y) |
| y-axis | (-x, y) |
| y = x | (y, x) |
| y = -x | (-y, -x) |
| x = a | (2a - x, y) |
| y = b | (x, 2b - y) |

We'll use these rules to find the new coordinates of each vertex after reflection.

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## ✔ Problem 1: Reflection across $ y = -2 $

- This is a horizontal line.
- The rule: For any point $ (x, y) $, its reflection over $ y = -2 $ is:
$$
(x, 2(-2) - y) = (x, -4 - y)
$$
- So, new y-coordinate = -4 - original y

Let’s suppose the triangle has vertices:
- $ J(-3, 0) $
- $ E(-5, -2) $
- $ Q(-1, -3) $
- $ Y(-2, -5) $

(You should verify these from your graph.)

Now apply transformation:

- $ J(-3, 0) \to (-3, -4 - 0) = (-3, -4) $
- $ E(-5, -2) \to (-5, -4 - (-2)) = (-5, -2) $
- $ Q(-1, -3) \to (-1, -4 - (-3)) = (-1, -1) $
- $ Y(-2, -5) \to (-2, -4 - (-5)) = (-2, 1) $

Plot these new points and connect them.

> 💡 Tip: The line $ y = -2 $ is the mirror. Each point is reflected so that the distance from the point to the line is preserved on the other side.

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## ✔ Problem 2: Reflection across the x-axis

- Rule: $ (x, y) \to (x, -y) $

Suppose quadrilateral $ MWD A $ has points:
- $ M(1, 3) $
- $ W(1, 2) $
- $ D(2, 3) $
- $ A(3, 1) $

Then:
- $ M(1,3) \to (1, -3) $
- $ W(1,2) \to (1, -2) $
- $ D(2,3) \to (2, -3) $
- $ A(3,1) \to (3, -1) $

Plot these and draw the reflected shape.

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## ✔ Problem 3: Reflection across $ y = -x $

- Rule: $ (x, y) \to (-y, -x) $

Suppose the kite-shaped figure has points:
- $ S(2, 3) $
- $ H(1, 0) $
- $ T(2, -3) $
- $ J(0, -1) $

Apply transformation:
- $ S(2,3) \to (-3, -2) $
- $ H(1,0) \to (0, -1) $
- $ T(2,-3) \to (3, -2) $
- $ J(0,-1) \to (1, 0) $

Note: This flips over the line $ y = -x $, which runs from top-left to bottom-right.

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## ✔ Problem 4: Reflection across $ y = -1 $

- Rule: $ (x, y) \to (x, 2(-1) - y) = (x, -2 - y) $

Suppose triangle $ IWL $ has:
- $ I(-3, 2) $
- $ W(-1, 4) $
- $ L(2, 1) $
- $ B(-3, -2) $

Wait — looks like quadrilateral $ IWB L $. Let's say:
- $ I(-3, 2) $
- $ W(-1, 4) $
- $ B(-3, -2) $
- $ L(2, 1) $

Reflect:
- $ I(-3,2) \to (-3, -2 - 2) = (-3, -4) $
- $ W(-1,4) \to (-1, -2 - 4) = (-1, -6) $
- $ B(-3,-2) \to (-3, -2 - (-2)) = (-3, 0) $
- $ L(2,1) \to (2, -2 - 1) = (2, -3) $

Plot these points.

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## ✔ Problem 5: Reflection across $ x = -3 $

- Rule: $ (x, y) \to (2(-3) - x, y) = (-6 - x, y) $

Suppose parallelogram $ WSPN $ has:
- $ W(-2, 3) $
- $ S(-1, 1) $
- $ P(-3, -1) $
- $ N(-4, 1) $

Apply:
- $ W(-2,3) \to (-6 - (-2), 3) = (-4, 3) $
- $ S(-1,1) \to (-6 - (-1), 1) = (-5, 1) $
- $ P(-3,-1) \to (-6 - (-3), -1) = (-3, -1) $ ← stays same (on line!)
- $ N(-4,1) \to (-6 - (-4), 1) = (-2, 1) $

So the image has points:
- $ (-4,3), (-5,1), (-3,-1), (-2,1) $

Plot and connect.

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## ✔ Problem 6: Reflection across $ y = x $

- Rule: $ (x, y) \to (y, x) $

Suppose triangle $ HQL $ has:
- $ H(-1, 3) $
- $ Q(-2, 1) $
- $ L(0, 2) $

Then:
- $ H(-1,3) \to (3, -1) $
- $ Q(-2,1) \to (1, -2) $
- $ L(0,2) \to (2, 0) $

Plot these new points and connect.

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## ✔ Summary: How to Solve Each Problem

For each figure:

1. Identify all vertices of the original figure.
2. Apply the reflection rule to each vertex.
3. Plot the new points on the grid.
4. Connect them in the same order as the original.

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## 🧩 Tips for Accuracy

- Use a ruler to draw lines between points.
- Double-check distances from the line of reflection.
- If a point lies on the line of reflection, it stays fixed.
- Label the image points clearly (e.g., $ J' $, $ E' $, etc.).

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If you can provide the coordinates of the original points for any specific problem (e.g., “Problem 1: J(-3,0), E(-5,-2), Q(-1,-3), Y(-2,-5)”), I can give you exact transformed coordinates and even sketch steps.

But based on standard Kuta Software problems, the above method applies perfectly.

Would you like me to generate a printable version of the solutions with labeled points? Or do you want to send the coordinates of one specific figure so I can solve it exactly?