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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: Now let's reflect (4, -5) over the x-axis. Which coordinate changes over the x-axis? The y-coordinate. What does -5 become when it changes sign? It becomes 5. The x stays 4, so the reflection is what point? It is (4, 5). Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

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

   1. AQuadrant II
   2. BQuadrant I
   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(1, 1)
   3. C(0, 1)
   4. D(1, 0)

   How do you know?

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(−3, 2)
   2. B(3, −2)
   3. C(−3, −2)
   4. D(2, 3)

   Why is that the answer?
2. 6

   Think it throughWhere is the ship after reflecting (3, 2) over the x-axis?

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

   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 x-coordinate
   2. BOnly the y-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?

Use the words

Fill each blank with a word from the bank.

• Reflecting across an axis keeps that coordinate and flips the ___ one.
• A flip of a point or shape over an axis to make a mirror image is a ___.
• The horizontal number line on the coordinate plane is the ___.
• The vertical number line on the coordinate plane is the ___.

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

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(5, -2)
   3. C(5, 2)
   4. D(2, -5)

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

   How do you know?
3. 14

   From Lesson 7.8Which location is in Quadrant III?

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

   How do you know?

Be honest — this tells your teacher what to do next