Reflections of triangles across the x-axis and y-axis on coordinate grids.

Let’s solve each problem step by step.

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Problem 3: Reflection across the x-axis

We are given triangle STU with points:

- S is at (1, 2)
- T is at (3, 4)
- U is at (5, 3)

*(Note: We read coordinates from the grid — x first, then y.)*

When we reflect a point across the x-axis, the rule is:

> (x, y) → (x, -y)

That means: keep the x-coordinate the same, flip the sign of the y-coordinate.

So let’s apply that to each point:

- S(1, 2) → S’(1, -2)
- T(3, 4) → T’(3, -4)
- U(5, 3) → U’(5, -3)

Now look at the answer choices for Problem 3:

- A) Triangle is still above x-axis → wrong
- B) Triangle is in second quadrant → wrong
- C) Points: S’ near (1,-2), T’ near (3,-4), U’ near (5,-3) → matches!
- D) Triangle is above x-axis again → wrong

✔ So correct answer for #3 is C

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Problem 4: Reflection across the y-axis

Given triangle CDE with points:

- C is at (-1, 5)
- D is at (-4, 4)
- E is at (-4, 1)

Rule for reflection across the y-axis:

> (x, y) → (-x, y)

Keep y the same, flip the sign of x.

Apply to each point:

- C(-1, 5) → C’(1, 5)
- D(-4, 4) → D’(4, 4)
- E(-4, 1) → E’(4, 1)

Now check answer choices for Problem 4:

- A) Points are in fourth quadrant? No — C’ should be at (1,5), which is top right. This one has C’ around (2,2)? Not matching.
- B) C’ at about (2,2), D’ at (1,1), E’ at (1,-3) → no
- C) All points on left side → that’s original or something else → no
- D) C’ at (1,5), D’ at (4,4), E’ at (4,1) → YES! Matches our calculation.

Wait — let me double-check D:

In option D:

- C’ is at (1,5) → yes
- D’ is at (4,4) → yes
- E’ is at (4,1) → yes

Perfect match.

✔ So correct answer for #4 is D

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Final Answer:
3) C
4) D