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

Lesson 7.97.9 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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.

Point B is the reflection of point A across the x-axis. B is at (−2.5, 4). Where is point A?

  1. Name the coordinate that changes across the x-axis: y changes sign
  2. Change the sign of y again: 4 → −4
  3. Keep x the same: −2.5 → −2.5
  4. Point A is at (−2.5, −4).
  5. Reflect (2, 3) across the x-axis. Then reflect that point across the y-axis.
  6. Reflect across the x-axis. Change the sign of y: (2, 3) → (2, −3)
  7. Reflect across the y-axis. Change the sign of x: (2, −3) → (−2, −3)
  8. Compare the first and last points: (2, 3) → (−2, −3)
  9. The final point is (−2, −3). Both coordinates changed sign.

Now you trySame steps, your turn

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

Reflect the point (4, −5) across the x-axis.

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 7.97.9 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    −5−4−3−2−112345−4−3−2−11234D (3.5, −2)
    C and D are mirror images across the y-axis.

    Point D is the reflection of point C across the y-axis. D is at (3.5, −2). Where is point C?

    1. 1Which coordinate changes across the y-axis?
    2. 2Change the sign of x back. What is the x-coordinate of C?
    3. 3What is the y-coordinate of C?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −5−4−3−2−112345−3−2−1123(−4, 1)
    Two flips, one across each axis.

    Reflect (−4, 1) across the y-axis. Then reflect that point across the x-axis.

    1. 1What is the x-coordinate after the first reflection?
    2. 2What is the y-coordinate after the second reflection?
    3. 3Why did both signs change from (−4, 1) to (4, −1)?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Reflect (0.5, −9) across the x-axis. What is the new y-coordinate?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Point M is reflected across the x-axis. Its image is at (−6, −3). What is the y-coordinate of M?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    −6−5−4−3−2−1123456−112345chest

    A pirate chest is buried at (−5, 4). A decoy chest is its reflection across the y-axis. How many units apart are the two chests?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Lu reflects (−8, 2) across the y-axis. She changes both signs. Which point is the correct reflection?

    1. A(8, 2)
    2. B(8, −2)
    3. C(−8, −2)
    4. D(2, −8)
    Show your work

Explain your thinkingLu changed both signs for one reflection. When does changing both signs work? Use a point and both axes to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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