Reflections worksheet for students to practice reflecting triangles across the x-axis and y-axis on a coordinate plane.

Here are the solutions to the reflection problems on the worksheet.

1. Reflect Triangle ABC across the x-axis

Step 1: Find the original points for Triangle ABC.
Looking at the graph, we identify the coordinates $(x, y)$ for each point:
* Point $A$ is at $(-2, 5)$.
* Point $B$ is at $(-4, 3)$.
* Point $C$ is at $(-1, 1)$.

Step 2: Apply the rule for reflecting across the x-axis.
When you reflect a shape across the horizontal x-axis, the x-coordinate stays the same, but the y-coordinate changes its sign (positive becomes negative, and negative becomes positive). The rule is: $(x, y) \rightarrow (x, -y)$.

Step 3: Calculate the new points.
* $A (-2, 5) \rightarrow A' (-2, -5)$
* $B (-4, 3) \rightarrow B' (-4, -3)$
* $C (-1, 1) \rightarrow C' (-1, -1)$

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2. Reflect Triangle EFG across the y-axis

Step 1: Find the original points for Triangle EFG.
Looking at the second graph:
* Point $E$ is at $(2, 2)$.
* Point $F$ is at $(6, 4)$.
* Point $G$ is at $(6, 0)$.

Step 2: Apply the rule for reflecting across the y-axis.
When you reflect a shape across the vertical y-axis, the y-coordinate stays the same, but the x-coordinate changes its sign. The rule is: $(x, y) \rightarrow (-x, y)$.

Step 3: Calculate the new points.
* $E (2, 2) \rightarrow E' (-2, 2)$
* $F (6, 4) \rightarrow F' (-6, 4)$
* $G (6, 0) \rightarrow G' (-6, 0)$

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3. Reflect Triangle XYZ across the x-axis

Step 1: Find the original points for Triangle XYZ.
Looking at the third graph:
* Point $X$ is at $(-2, -1)$.
* Point $Y$ is at $(-4, -3)$.
* Point $Z$ is at $(-1, -5)$.

Step 2: Apply the rule for reflecting across the x-axis.
Just like in problem #1, the x-coordinate stays the same, and the y-coordinate flips its sign. Since all these y-coordinates are negative, they will become positive. Rule: $(x, y) \rightarrow (x, -y)$.

Step 3: Calculate the new points.
* $X (-2, -1) \rightarrow X' (-2, 1)$
* $Y (-4, -3) \rightarrow Y' (-4, 3)$
* $Z (-1, -5) \rightarrow Z' (-1, 5)$

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Final Answer:

1. Reflection of Triangle ABC across the x-axis:
* $A (-2, 5) \quad A' (-2, -5)$
* $B (-4, 3) \quad B' (-4, -3)$
* $C (-1, 1) \quad C' (-1, -1)$

2. Reflection of Triangle EFG across the y-axis:
* $E (2, 2) \quad E' (-2, 2)$
* $F (6, 4) \quad F' (-6, 4)$
* $G (6, 0) \quad G' (-6, 0)$

3. Reflection of Triangle XYZ across the x-axis:
* $X (-2, -1) \quad X' (-2, 1)$
* $Y (-4, -3) \quad Y' (-4, 3)$
* $Z (-1, -5) \quad Z' (-1, 5)$