Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.9Reflect Points Across Axes

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can reflect points across the x-axis and y-axis on the coordinate plane.

Why This Matters Captain Vega discovers that her treasure map has a magic mirror trick! When she folds the map along the x-axis, some clues match up perfectly with clues on the other side. For example, a marker at (2, 4) has a matching marker at (2, -4) when reflected over the x-axis. Another pair reflects over the y-axis: (5, 3) and (-5, 3). How does reflection change the coordinates?

RememberReflect Points Across Axes

Reflections Across Axes. Formula: Reflect over x-axis: (x, y) → (x, −y) | Reflect over y-axis: (x, y) → (−x, y) A reflection is a flip of a point over a line, like a mirror image. The axis you flip over decides which coordinate changes its sign.

  1. Reflection across x-axis (horizontal line): y-coordinate changes sign, x stays same.
  2. Reflection across y-axis (vertical line): x-coordinate changes sign, y stays same.
  3. Both coordinates change sign when reflecting across both axes: (−x, −y)

Words: Reflection (Reflexión)x-axis (Eje x)y-axis (Eje y)Symmetry (Simetría)Integer (Número entero)

  1. 1Circle the letter of the best answer. Show how you know.

    In which quadrant is the point (−4, 5)?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant III
    4. DQuadrant IV
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which point lies ON the y-axis?

    1. A(0, 3)
    2. B(3, 0)
    3. C(3, 3)
    4. D(−3, 1)
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What are the coordinates of the origin?

    1. A(0, 0)
    2. B(0, 1)
    3. C(1, 1)
    4. D(1, 0)
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A point has a negative x-coordinate and a negative y-coordinate. Which quadrant is it in?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant III
    4. DQuadrant IV
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A game designer creates a spaceship at (3, 2) and wants to place enemy ships as reflections to make the level symmetric. One enemy is reflected over the y-axis, and another is reflected over the x-axis. Where is the ship after reflecting (3, 2) over the y-axis?

    1. A(2, 3)
    2. B(−3, 2)
    3. C(3, −2)
    4. D(−3, −2)
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A game designer creates a spaceship at (3, 2) and wants to place enemy ships as reflections to make the level symmetric. One enemy is reflected over the y-axis, and another is reflected over the x-axis. Where is the ship after reflecting (3, 2) over the x-axis?

    1. A(2, 3)
    2. B(3, −2)
    3. C(−3, 2)
    4. D(−3, −2)
    Show your work

Explain your thinkingWhat pattern do you notice about the coordinates when reflecting over the x-axis versus the y-axis?

Sentence starter When I reflect over the x-axis, the ___ -coordinate changes sign and the ___ -coordinate stays the same. When I reflect over the y-axis, the ___ -coordinate changes sign and the ___ -coordinate stays the same.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.9Reflect Points Across Axes

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can reflect points across the x-axis and y-axis on the coordinate plane.

Why This Matters Captain Vega discovers that her treasure map has a magic mirror trick! When she folds the map along the x-axis, some clues match up perfectly with clues on the other side. For example, a marker at (2, 4) has a matching marker at (2, -4) when reflected over the x-axis. Another pair reflects over the y-axis: (5, 3) and (-5, 3). How does reflection change the coordinates?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each map marker and fold line to its mirror image.

    1. (1, 7) folded over x-axis
    2. (-8, 2) folded over y-axis
    3. (9, -3) folded over x-axis
    4. (-1, -6) folded over y-axis
    • A(1, -7)
    • B(8, 2)
    • C(9, 3)
    • D(1, -6)
  2. 2Write the name of the correct group on each line.

    Sort each fold by which coordinate rule it follows on Vega's map.

    Groups: Over x-axis: keep x, flip y (x, -y) Over y-axis: flip x, keep y (-x, y)
    • (4, 9) fold over x-axis
    • (-2, 5) fold over x-axis
    • (6, -1) fold over x-axis
    • (3, 8) fold over y-axis
    • (-7, 4) fold over y-axis
    • (2, -9) fold over y-axis
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A game designer creates a spaceship at (3, 2) and wants to place enemy ships as reflections to make the level symmetric. One enemy is reflected over the y-axis, and another is reflected over the x-axis. Reflecting over the y-axis changes which coordinate?

    1. AOnly the y-coordinate
    2. BOnly the x-coordinate
    3. CBoth coordinates
    4. DNeither coordinate
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Captain Vega folds the map along the x-axis. A marker at (7, 2) lands on its mirror image. What are the new coordinates?

    1. A(-7, 2)
    2. B(-7, -2)
    3. C(2, 7)
    4. D(7, -2)
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A buried chest is marked at (-5, 3). Vega folds the map along the y-axis to find its mirror twin. Where is the twin?

    1. A(-5, -3)
    2. B(3, -5)
    3. C(5, 3)
    4. D(5, -3)
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Vega reflects a palm-tree marker at (8, -6) across the x-axis. Which coordinate changes its sign?

    1. AThe x-coordinate
    2. BThe y-coordinate
    3. CBoth coordinates
    4. DNeither coordinate
    Show your work

Explain your thinkingWhat pattern do you notice about the coordinates when reflecting over the x-axis versus the y-axis?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help