Kuta Software Lesson Plans & Worksheets Reviewed by Teachers - Free Printable

Since the user has not requested explanations, topic teaching, or practice tasks (all set to false), and the task is to graph reflections — which cannot be visually rendered in text — I will instead provide the coordinates of the reflected points for each problem. This allows the student to plot them accurately on their grid.

Let’s go step by step:

---

Problem 1: Reflection across the x-axis

Original points (from graph):
- P is at (1, 2)
- Q is at (3, -1)
- R is at (2, 3)

Reflection over x-axis: (x, y) → (x, -y)

So:
- P’ = (1, -2)
- Q’ = (3, 1)
- R’ = (2, -3)

---

Problem 2: Reflection across y = 3

Original points:
- S is at (-2, 2)
- T is at (-1, 4)
- U is at (1, 4)

To reflect over horizontal line y = k: new y = 2k - original y

Here k = 3, so new y = 6 - original y

- S: y=2 → 6-2=4 → S’ = (-2, 4)
- T: y=4 → 6-4=2 → T’ = (-1, 2)
- U: y=4 → 6-4=2 → U’ = (1, 2)

---

Problem 3: Reflection across y = 1

Original points:
- F is at (-3, 2)
- G is at (-4, 0)
- H is at (-1, 1)

k = 1 → new y = 2(1) - y = 2 - y

- F: y=2 → 2-2=0 → F’ = (-3, 0)
- G: y=0 → 2-0=2 → G’ = (-4, 2)
- H: y=1 → 2-1=1 → H’ = (-1, 1) ← stays same since it's on the line

---

Problem 4: Reflection across the x-axis

Original points:
- A is at (2, 2)
- B is at (3, 0)
- C is at (2, -1)
- D is at (3, 3)

Reflect over x-axis: (x, y) → (x, -y)

- A’ = (2, -2)
- B’ = (3, 0) ← stays same
- C’ = (2, 1)
- D’ = (3, -3)

---

Problem 5: Reflection across the x-axis

Given points:
- T(2, 2)
- C(2, 5)
- J(5, 4)
- F(5, 0)

Reflect over x-axis: (x, y) → (x, -y)

- T’ = (2, -2)
- C’ = (2, -5)
- J’ = (5, -4)
- F’ = (5, 0) ← stays same

---

Problem 6: Reflection across y = -2

Given points:
- B(-1, -5)
- M(-1, -4)
- R(1, -2)
- C(3, -3)

k = -2 → new y = 2*(-2) - y = -4 - y

- B: y=-5 → -4 - (-5) = 1 → B’ = (-1, 1)
- M: y=-4 → -4 - (-4) = 0 → M’ = (-1, 0)
- R: y=-2 → -4 - (-2) = -2 → R’ = (1, -2) ← stays same
- C: y=-3 → -4 - (-3) = -1 → C’ = (3, -1)

---

Final Answer:
1) P'(1, -2), Q'(3, 1), R'(2, -3)
2) S'(-2, 4), T'(-1, 2), U'(1, 2)
3) F'(-3, 0), G'(-4, 2), H'(-1, 1)
4) A'(2, -2), B'(3, 0), C'(2, 1), D'(3, -3)
5) T'(2, -2), C'(2, -5), J'(5, -4), F'(5, 0)
6) B'(-1, 1), M'(-1, 0), R'(1, -2), C'(3, -1)