6.NOS.7 Group 2 · Challenge

Practice Set · Part 1

Reflect Points Across Axes

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: 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.

The big idea: Each reflection changes the sign of one coordinate, so you can undo a reflection or combine two of them.

Model to copy — Example 1 · Work backward

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

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

  1. 1

    Same stepsFinish what the group started. Use the model above, step for step.

    Try it together — then prove it: Reflect the point (4, −5) across the x-axis. Which coordinate changes across the x-axis? What does it become? (y changes: −5 becomes 5.) What is the new point? ((4, 5)) Why does x stay 4 when you reflect across the x-axis? (The point flips up or down over the x-axis. It does not move left or right, so x stays 4.)
    Show your work
  2. 2

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

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant III
    4. DQuadrant IV

    How do you know?

  3. 3

    Warm restartWhich point lies ON the y-axis?

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

    How do you know?

  4. 4

    Warm restartWhat are the coordinates of the origin?

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

    How do you know?

7.9 Small Group · Group 2 · Practice SetPart 1 of 4
6.NOS.7 Group 2 · Challenge

Practice Set · Part 2

Reflect Points Across Axes

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

  1. 5

    Think it throughWhere 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)

    Why is that the answer?

  2. 6

    Think it throughWhere 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)

    How do you know? Give a second reason as well.

  3. 7

    Think it throughReflecting over the y-axis changes which coordinate?

    1. AOnly the y-coordinate
    2. BOnly the x-coordinate
    3. CBoth coordinates
    4. DNeither coordinate

    Explain your thinking. What would have to change for a different choice to be right?

  4. 8

    Back to the modelWhat pattern do you notice about the coordinates when reflecting over the x-axis versus the y-axis?

7.9 Small Group · Group 2 · Practice SetPart 2 of 4
6.NOS.7 Group 2 · Challenge

Practice Set · Part 3

Reflect Points Across Axes

Words and reasoning

Word bank · Banco de palabras

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

Use the words

Fill each blank with a word from the bank.

Explain the thinking

  1. 9

    Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

    The 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).
  2. 10

    Say moreReflect (4, -5) over the x-axis. Talk through how the coordinates change and where the new point lands.

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Captain Vega folds her treasure map along the x-axis. A lookout tower is marked at (5, 2), and after the fold, a matching tower symbol lines up at (5, -2) on the other side of the fold line.

    Show your work
7.9 Small Group · Group 2 · Practice SetPart 3 of 4
6.NOS.7 Group 2 · Challenge

Practice Set · Part 4

Reflect Points Across Axes

Show what you know

Last check

These two come from Lesson 7.8. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — What is the reflection of (-5, 2) over the y-axis?

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

    Explain your choice.

  2. 13

    From Lesson 7.8Explain your thinking — A point has a negative x-coordinate and a negative y-coordinate. Which quadrant is it in?

    1. AQuadrant III
    2. BQuadrant I
    3. CQuadrant II
    4. DQuadrant IV

    How do you know?

  3. 14

    From Lesson 7.8Which location is in Quadrant III?

    1. ACity Hall (0, 0)
    2. BThe school (2, 3)
    3. CThe library (−3, 4)
    4. DThe hospital (−4, −1)

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
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.
I can explain why it works: Each reflection changes the sign of one coordinate, so you can undo a reflection or combine two of them.
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time