Practice graphing reflections of geometric shapes on a coordinate plane.

Let's solve each of the four reflection problems step by step. We'll determine the coordinates of the original points, apply the correct reflection rule, and then plot the image.

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1. Reflect trapezoid QRST across the y-axis

Step 1: Identify the coordinates of QRST
From the graph:
- Q = (-8, -3)
- R = (-5, -3)
- S = (-4, -6)
- T = (-9, -6)

Reflection across the y-axis:
The rule is:
> (x, y) → (-x, y)

Apply this to each point:
- Q(-8, -3) → Q'(8, -3)
- R(-5, -3) → R'(5, -3)
- S(-4, -6) → S'(4, -6)
- T(-9, -6) → T'(9, -6)

Plot these new points and connect them in order to form the reflected trapezoid Q'R'S'T'.

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2. Reflect rectangle ABCD over the line y = 3

Step 1: Identify the coordinates of ABCD
From the graph:
- A = (-3, 4)
- B = (-3, 8)
- C = (-7, 8)
- D = (-7, 4)

Reflection over the line y = 3:
To reflect a point over a horizontal line y = k, use:
> The distance from the point to the line y = 3 is |y - 3|, so the reflected point will be on the opposite side at the same distance.

So:
> (x, y) → (x, 2×3 - y) = (x, 6 - y)

Apply this:
- A(-3, 4) → A'(-3, 6 - 4) = (-3, 2)
- B(-3, 8) → B'(-3, 6 - 8) = (-3, -2)
- C(-7, 8) → C'(-7, 6 - 8) = (-7, -2)
- D(-7, 4) → D'(-7, 6 - 4) = (-7, 2)

Plot these points and connect them to form the reflected rectangle A'B'C'D'.

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3. Reflect parallelogram WXYZ across the x-axis

Step 1: Identify the coordinates of WXYZ
From the graph:
- W = (-4, 4)
- X = (0, 6)
- Y = (-5, 6)
- Z = (-8, 4)

Reflection across the x-axis:
Rule:
> (x, y) → (x, -y)

Apply:
- W(-4, 4) → W'(-4, -4)
- X(0, 6) → X'(0, -6)
- Y(-5, 6) → Y'(-5, -6)
- Z(-8, 4) → Z'(-8, -4)

Plot these points and connect to form W'X'Y'Z'.

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4. Reflect trapezoid JKLM over the line x = 2

Step 1: Identify the coordinates of JKLM
From the graph:
- J = (-2, -6)
- K = (-4, -4)
- L = (0, -4)
- M = (2, -6)

Reflection over the vertical line x = 2:
Rule:
> Distance from x-coordinate to 2 is |x - 2|, so the reflected x-coordinate is:
> x' = 2×2 - x = 4 - x

So:
> (x, y) → (4 - x, y)

Apply:
- J(-2, -6) → J'(4 - (-2), -6) = (6, -6)
- K(-4, -4) → K'(4 - (-4), -4) = (8, -4)
- L(0, -4) → L'(4 - 0, -4) = (4, -4)
- M(2, -6) → M'(4 - 2, -6) = (2, -6)

Note: M is on the line x = 2, so it stays the same.

Plot these points and connect to form the reflected trapezoid J'K'L'M'.

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✔ Summary of Reflection Rules Used:

| Reflection Type | Rule |
|----------------------------|-----------------------------|
| Over y-axis | (x, y) → (-x, y) |
| Over x-axis | (x, y) → (x, -y) |
| Over line y = k | (x, y) → (x, 2k - y) |
| Over line x = h | (x, y) → (2h - x, y) |

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🔧 Final Answer:

You should now:
- Plot each reflected figure using the transformed coordinates.
- Connect the points in the same order as the original.
- Label the images clearly (e.g., Q'R'S'T', etc.).

Let me know if you'd like a visual sketch or help plotting them!