Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Reflect the point (4, −5) across the x-axis.
   2. Which coordinate changes across the x-axis? What does it become? (y changes: −5 becomes 5.)
   3. What is the new point? ((4, 5))
   4. 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

   Quick reviewIn which quadrant is the point (−4, 5)? 🔊 Listen 💡 Hint

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

   How do you know?
3. 3

   Quick reviewWhich point lies ON the y-axis? 🔊 Listen 💡 Hint

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

   How do you know?
4. 4

   Quick reviewWhat are the coordinates of the origin? 🔊 Listen 💡 Hint

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

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhere is the ship after reflecting (3, 2) over the y-axis? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• 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 ___.
• When two halves are mirror images of each other, the figure has ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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. 🔊 Listen 💡 Hint
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. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

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

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.