Reflections (A) worksheet with four geometric figures to reflect over specified axes.

To solve this problem, we need to draw the reflection of each shape across the given line. Here is how reflections work:

1. Reflect over $y = 0$ (the x-axis): This is like flipping the shape upside down. The top part goes to the bottom, and the bottom part goes to the top. The horizontal position (left/right) stays exactly the same.
* Mathematically: If a point is at $(x, y)$, its reflection is at $(x, -y)$.

2. Reflect over $x = 0$ (the y-axis): This is like flipping the shape sideways (like turning a page in a book). The right side goes to the left, and the left side goes to the right. The vertical height (up/down) stays exactly the same.
* Mathematically: If a point is at $(x, y)$, its reflection is at $(-x, y)$.

Let's go through each graph one by one.

Graph 1 (Top Left): Reflect over $y = 0$
* Original Shape: A triangle with vertices roughly at $(-4, 1)$, $(-1, 1)$, and $(1, 5)$.
* Reflection Rule: Keep the x-coordinate, flip the sign of the y-coordinate.
* New Vertices:
* $(-4, 1)$ becomes $(-4, -1)$.
* $(-1, 1)$ becomes $(-1, -1)$.
* $(1, 5)$ becomes $(1, -5)$.
* Drawing: Draw a triangle connecting these new points. It will look like the original triangle flipped upside down below the x-axis.

Graph 2 (Top Right): Reflect over $x = 0$
* Original Shape: A triangle with vertices roughly at $(1, -3)$, $(4, -2)$, and $(2, 4)$.
* Reflection Rule: Flip the sign of the x-coordinate, keep the y-coordinate.
* New Vertices:
* $(1, -3)$ becomes $(-1, -3)$.
* $(4, -2)$ becomes $(-4, -2)$.
* $(2, 4)$ becomes $(-2, 4)$.
* Drawing: Draw a triangle connecting these new points. It will look like the original triangle flipped horizontally to the left side of the y-axis.

Graph 3 (Bottom Left): Reflect over $x = 0$
* Original Shape: A triangle with vertices roughly at $(2, 0)$, $(4, 3)$, and $(3, 4)$.
* Reflection Rule: Flip the sign of the x-coordinate, keep the y-coordinate.
* New Vertices:
* $(2, 0)$ becomes $(-2, 0)$.
* $(4, 3)$ becomes $(-4, 3)$.
* $(3, 4)$ becomes $(-3, 4)$.
* Drawing: Draw a triangle connecting these new points. It will be on the left side of the y-axis, mirroring the original shape.

Graph 4 (Bottom Right): Reflect over $y = 0$
* Original Shape: A triangle with vertices roughly at $(-4, -1)$, $(4, -1)$, and $(0, 2)$.
* Reflection Rule: Keep the x-coordinate, flip the sign of the y-coordinate.
* New Vertices:
* $(-4, -1)$ becomes $(-4, 1)$.
* $(4, -1)$ becomes $(4, 1)$.
* $(0, 2)$ becomes $(0, -2)$.
* Drawing: Draw a triangle connecting these new points. The base which was below the axis is now above it, and the peak which was above is now below.

Final Answer:
The solution involves drawing four new triangles on the grids based on the reflection rules:

1. Top Left Grid: Draw a triangle with corners at $(-4, -1)$, $(-1, -1)$, and $(1, -5)$.
2. Top Right Grid: Draw a triangle with corners at $(-1, -3)$, $(-4, -2)$, and $(-2, 4)$.
3. Bottom Left Grid: Draw a triangle with corners at $(-2, 0)$, $(-4, 3)$, and $(-3, 4)$.
4. Bottom Right Grid: Draw a triangle with corners at $(-4, 1)$, $(4, 1)$, and $(0, -2)$.