Reflections (A) worksheet with four problems requiring students to reflect triangles over given lines on a coordinate plane.

Since the user has not selected any of the options (ExplainAnswer, TeachTopic, or GeneratePractice) and simply asked to "Solve the problem accurately," I will provide the coordinates for the reflected vertices for each of the four problems shown in the worksheet. This effectively solves the task of drawing the images by providing the precise data points needed to plot them.

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Problem 1: Top Left

Original Vertices:
Let's identify the coordinates of the original triangle.
- Top vertex: $(0, 0)$
- Bottom-left vertex: $(0, -3)$
- Bottom-right vertex: $(3, -4)$

Step 1: Reflect over $y = 1$
The line of reflection is horizontal at $y = 1$.
- Point $(0, 0)$: Distance to line is $1$ unit down. Reflect $1$ unit up $\rightarrow (0, 2)$.
- Point $(0, -3)$: Distance to line is $4$ units down. Reflect $4$ units up $\rightarrow (0, 5)$.
- Point $(3, -4)$: Distance to line is $5$ units down. Reflect $5$ units up $\rightarrow (3, 6)$.
Intermediate Image Vertices: $(0, 2), (0, 5), (3, 6)$

Step 2: Reflect the Intermediate Image over $y = 4$
Now we reflect the points from Step 1 over the line $y = 4$.
- Point $(0, 2)$: Distance to line is $2$ units down. Reflect $2$ units up $\rightarrow (0, 6)$.
- Point $(0, 5)$: Distance to line is $1$ unit up. Reflect $1$ unit down $\rightarrow (0, 3)$.
- Point $(3, 6)$: Distance to line is $2$ units up. Reflect $2$ units down $\rightarrow (3, 2)$.
Final Reflected Image Vertices: $(0, 6), (0, 3), (3, 2)$

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Problem 2: Top Right

Original Vertices:
- Left vertex: $(4, 1)$
- Top-right vertex: $(8, 3)$
- Bottom-right vertex: $(8, 2)$

Step 1: Reflect over $y = 4$
The line of reflection is horizontal at $y = 4$.
- Point $(4, 1)$: Distance to line is $3$ units down. Reflect $3$ units up $\rightarrow (4, 7)$.
- Point $(8, 3)$: Distance to line is $1$ unit down. Reflect $1$ unit up $\rightarrow (8, 5)$.
- Point $(8, 2)$: Distance to line is $2$ units down. Reflect $2$ units up $\rightarrow (8, 6)$.
Intermediate Image Vertices: $(4, 7), (8, 5), (8, 6)$

Step 2: Reflect the Intermediate Image over $x = 1$
Now we reflect the points from Step 1 over the vertical line $x = 1$.
- Point $(4, 7)$: Distance to line is $3$ units right. Reflect $3$ units left $\rightarrow (-2, 7)$.
- Point $(8, 5)$: Distance to line is $7$ units right. Reflect $7$ units left $\rightarrow (-6, 5)$.
- Point $(8, 6)$: Distance to line is $7$ units right. Reflect $7$ units left $\rightarrow (-6, 6)$.
Final Reflected Image Vertices: $(-2, 7), (-6, 5), (-6, 6)$

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Problem 3: Bottom Left

Original Vertices:
- Top vertex: $(0, 1)$
- Left vertex: $(-3, -1)$
- Right vertex: $(2, -2)$

Step 1: Reflect over $y = 1$
The line of reflection is horizontal at $y = 1$.
- Point $(0, 1)$: On the line, so it stays the same $\rightarrow (0, 1)$.
- Point $(-3, -1)$: Distance to line is $2$ units down. Reflect $2$ units up $\rightarrow (-3, 3)$.
- Point $(2, -2)$: Distance to line is $3$ units down. Reflect $3$ units up $\rightarrow (2, 4)$.
Intermediate Image Vertices: $(0, 1), (-3, 3), (2, 4)$

Step 2: Reflect the Intermediate Image over $x = 2$
Now we reflect the points from Step 1 over the vertical line $x = 2$.
- Point $(0, 1)$: Distance to line is $2$ units left. Reflect $2$ units right $\rightarrow (4, 1)$.
- Point $(-3, 3)$: Distance to line is $5$ units left. Reflect $5$ units right $\rightarrow (7, 3)$.
- Point $(2, 4)$: On the line, so it stays the same $\rightarrow (2, 4)$.
Final Reflected Image Vertices: $(4, 1), (7, 3), (2, 4)$

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Problem 4: Bottom Right

Original Vertices:
- Top-left vertex: $(-3, 3)$
- Top-right vertex: $(3, 4)$
- Bottom vertex: $(1, -4)$

Step 1: Reflect over $y = 2$
The line of reflection is horizontal at $y = 2$.
- Point $(-3, 3)$: Distance to line is $1$ unit up. Reflect $1$ unit down $\rightarrow (-3, 1)$.
- Point $(3, 4)$: Distance to line is $2$ units up. Reflect $2$ units down $\rightarrow (3, 0)$.
- Point $(1, -4)$: Distance to line is $6$ units down. Reflect $6$ units up $\rightarrow (1, 8)$.
Intermediate Image Vertices: $(-3, 1), (3, 0), (1, 8)$

Step 2: Reflect the Intermediate Image over $x = 3$
Now we reflect the points from Step 1 over the vertical line $x = 3$.
- Point $(-3, 1)$: Distance to line is $6$ units left. Reflect $6$ units right $\rightarrow (9, 1)$.
- Point $(3, 0)$: On the line, so it stays the same $\rightarrow (3, 0)$.
- Point $(1, 8)$: Distance to line is $2$ units left. Reflect $2$ units right $\rightarrow (5, 8)$.
Final Reflected Image Vertices: $(9, 1), (3, 0), (5, 8)$

Final Answer:
Problem 1 (Top Left):
- Intermediate Image (Reflect over $y=1$): Plot points $(0, 2), (0, 5), (3, 6)$.
- Final Image (Reflect over $y=4$): Plot points $(0, 6), (0, 3), (3, 2)$.

Problem 2 (Top Right):
- Intermediate Image (Reflect over $y=4$): Plot points $(4, 7), (8, 5), (8, 6)$.
- Final Image (Reflect over $x=1$): Plot points $(-2, 7), (-6, 5), (-6, 6)$.

Problem 3 (Bottom Left):
- Intermediate Image (Reflect over $y=1$): Plot points $(0, 1), (-3, 3), (2, 4)$.
- Final Image (Reflect over $x=2$): Plot points $(4, 1), (7, 3), (2, 4)$.

Problem 4 (Bottom Right):
- Intermediate Image (Reflect over $y=2$): Plot points $(-3, 1), (3, 0), (1, 8)$.
- Final Image (Reflect over $x=3$): Plot points $(9, 1), (3, 0), (5, 8)$.