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

Lesson 7.9Reflect Points Across Axes

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ReflectionSpanish: Reflexión A flipped, mirror image across a line. (3, 2) reflected over the y-axis becomes (-3, 2) — x changes sign, y stays
x-axisSpanish: Eje x The line that goes across the grid. Flipping over it changes the y sign. (4, 3) → (4, -3): the y flips from +3 to -3, like folding the paper along the horizontal line
y-axisSpanish: Eje y The line that goes up the grid. Flipping over it changes the x sign. (4, 3) → (-4, 3): the x flips from +4 to -4, like folding the paper along the vertical line
SymmetrySpanish: Simetría When a shape looks the same on both sides of a line. A butterfly's wings are symmetric — fold it down the middle and both sides match
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ..., -3, -2, -1, 0, 1, 2, 3, ...
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The dashed height meets the base at a square corner — the small 90° box is what makes it perpendicular, not slanted.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

I will reflect (3, 2) over the y-axis.

  1. The y-axis is the vertical line, so the point flips left or right. That changes the x-coordinate.
  2. The x changes sign: 3 becomes -3. The y stays the same: 2 stays 2.
  3. So the reflection of (3, 2) over the y-axis is (-3, 2).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Now let's reflect (4, -5) over the x-axis. Which coordinate changes over the x-axis? The y-coordinate.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • 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.

Word bank Reflectionx-axisy-axisSymmetryIntegerPerpendicularreflectoppositesignchangesamemirror

Watch outA common mistake

A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate — changing the x-coordinate when reflecting over the x-axis, instead of the y-coordinate (or vice versa for the y-axis). For example, to reflect (3, -5) over the x-axis, a student might flip the x-coordinate and write (-3, -5), but reflecting over the x-axis only changes the sign of the y-coordinate: (3, -5) becomes (3, 5). Before you submit, ask: 'Did I flip the sign of the coordinate that matches the axis I'm reflecting over — y for the x-axis, x for the y-axis?'

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

Lesson 7.9Reflect Points Across Axes

Version ASupported 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.

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

    Match each point and axis to its reflection.

    1. (2, 5) over y-axis
    2. (-3, 1) over y-axis
    3. (4, -6) over x-axis
    4. (-1, -4) over x-axis
    5. (5, 2) over x-axis
    6. (-6, 3) over y-axis
    • A(-2, 5)
    • B(3, 1)
    • C(4, 6)
    • D(-1, 4)
    • E(5, -2)
    • F(6, 3)

    Hint Read the axis on each card: the y-axis flips the x sign; the x-axis flips the y sign. Only ONE number changes.

  2. 2Write the name of the correct group on each line.

    Put the steps in order for reflecting (5, -3) over the y-axis.

    Groups:
    • Start with the point (5, -3)
    • Identify the axis of reflection: y-axis
    • The y-axis is vertical, so the x-coordinate changes sign
    • Change x from 5 to -5, keep y as -3
    • The reflection is (-5, -3)

    Hint The steps tell a story: start with the point, identify the axis, apply the rule, then state the result.

Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    What is the reflection of (4, -3) over the x-axis?

    1. A(-4, -3)
    2. B(-4, 3)
    3. C(3, -4)
    4. D(4, 3)

    Hint Reflecting over the x-axis flips the point UP/DOWN — the left/right position doesn't move.

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    What is the reflection of (-2, 6) over the y-axis?

    1. A(-2, -6)
    2. B(2, 6)
    3. C(2, -6)
    4. D(6, -2)

    Hint Reflecting over the y-axis flips LEFT/RIGHT — the height stays the same.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Which point is on the y-axis?

    1. A(-2, 4)
    2. B(0, 5)
    3. C(3, 3)
    4. D(5, 0)

    Hint Points on the y-axis have gone 0 units left or right — check the FIRST coordinate.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemReflect the point (6, 4) over the y-axis.
    2. 2AttemptThe y-axis is vertical, so I will change the y-coordinate: 4 becomes -4. The answer is (6, -4).
    3. 3CheckThe point only moved up and down, but a fold over the vertical y-axis should move it left and right.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The y-axis is the vertical line. Folding over it moves a point left or right, so the x-coordinate is what changes.

    Correct work
    Correct answer:

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.

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

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Plot and label each point on the grid.

    Plot (1, 4) and its reflections: over the x-axis, over the y-axis, and over both axes

    -6-4-20246-6-4-20246xy
    Show your thinking
  2. 2Complete the table. Show how you found each value.

    Find the reflection of each point over the given axis.

    Original PointAxisReflected Point
    (3, -7)x-axis
    (-5, 2)y-axis
    (8, -1)x-axis
    (-4, -6)y-axis
    (0, 9)x-axis
    (-3, 0)y-axis
    Show your work
  3. 3Write the letter of the matching item on each line.

    Match each reflection rule to its description.

    1. Over x-axis
    2. Over y-axis
    3. Over both axes
    4. Point on x-axis
    5. Point on y-axis
    6. (0, 0)
    • Ay-coordinate changes sign
    • Bx-coordinate changes sign
    • CBoth coordinates change sign
    • DReflects to itself over x-axis
    • EReflects to itself over y-axis
    • FReflects to itself over any axis
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Point A is at (-3, 5). It is reflected over the x-axis to A', then A' is reflected over the y-axis to A''. What are the coordinates of A''?

    1. A(-3, -5)
    2. B(-3, 5)
    3. C(3, -5)
    4. D(3, 5)
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemReflect the point (-3, -8) over the x-axis.
    2. 2AttemptBoth coordinates are negative, so I will flip the x-coordinate: -3 becomes 3. The answer is (3, -8).
    3. 3CheckFolding over the horizontal x-axis should send the point up across the axis, but this answer kept it below the axis.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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

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

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Plot and label each point on the grid.

    Plot the point (-2, 3). Reflect it over the x-axis, then reflect that result over the y-axis. Where do you end up? Now start over and reflect (-2, 3) over the y-axis first, then over the x-axis. Do you get the same final point?

    -5-4-3-2-1012345-5-4-3-2-1012345xy
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Reflection Error

    1. 1ProblemReflect (-3, 5) over the y-axis
    2. 2Student thinkingThe y-axis is vertical, so I change the y-coordinate
    3. 3Student answer(-3, -5)

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A triangle has vertices at A(1, 2), B(4, 2), and C(4, 6). If you reflect the entire triangle over the y-axis, what are the new vertices? What do you notice about the size and shape of the reflected triangle compared to the original?

    Write your answer

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

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help