Lesson 7.9Reflect Points Across Axes
Start hereWords, worked example, and sentence starters
Learning target I can reflect points across the x-axis and y-axis on the coordinate plane.
Why This Matters Captain Vega discovers that her treasure map has a magic mirror trick! When she folds the map along the x-axis, some clues match up perfectly with clues on the other side. For example, a marker at (2, 4) has a matching marker at (2, -4) when reflected over the x-axis. Another pair reflects over the y-axis: (5, 3) and (-5, 3). How does reflection change the coordinates?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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.
- The y-axis is the vertical line, so the point flips left or right. That changes the x-coordinate.
- The x changes sign: 3 becomes -3. The y stays the same: 2 stays 2.
- 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.
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 out!A common mistake
A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate
Lesson 7.9Reflect Points Across Axes
Level 0Most support · every hint printed
Learning target I can reflect points across the x-axis and y-axis on the coordinate plane.
Why This Matters Captain Vega discovers that her treasure map has a magic mirror trick! When she folds the map along the x-axis, some clues match up perfectly with clues on the other side. For example, a marker at (2, 4) has a matching marker at (2, -4) when reflected over the x-axis. Another pair reflects over the y-axis: (5, 3) and (-5, 3). How does reflection change the coordinates?
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.
- The y-axis is the vertical line, so the point flips left or right. That changes the x-coordinate.
- The x changes sign: 3 becomes -3. The y stays the same: 2 stays 2.
- So the reflection of (3, 2) over the y-axis is (-3, 2).
-
1Write the letter of the matching item on each line.
Match each point and axis to its reflection.
- (2, 5) over y-axis
- (-3, 1) over y-axis
- (4, -6) over x-axis
- (-1, -4) over x-axis
- (5, 2) over x-axis
- (-6, 3) over y-axis
- A(-2, 5)
- B(3, 1)
- C(4, 6)
- D(-1, 4)
- E(5, -2)
- F(6, 3)
Steps to try- Read the axis on each card: the y-axis flips the x sign; the x-axis flips the y sign. Only ONE number changes.
- For each card, copy the pair, flip the correct coordinate's sign, and find that result among the matches.
- Try '(2, 5) over y-axis': flip the 2's sign and keep the 5. Find the match that shows exactly that change.
-
2Circle the letter of the best answer. Show how you know.
What is the reflection of (4, -3) over the x-axis?
- A(-4, -3)
- B(-4, 3)
- C(3, -4)
- D(4, 3)
Steps to try- Reflecting over the x-axis flips the point UP/DOWN — the left/right position doesn't move.
- Keep the x-coordinate the same and switch the sign of the y-coordinate. Don't swap the numbers' order.
- The point sits 3 units below the x-axis. Its mirror sits the same 3 units above, with the x still 4.
Show your work -
3Circle the letter of the best answer. Show how you know.
What is the reflection of (-2, 6) over the y-axis?
- A(-2, -6)
- B(2, 6)
- C(2, -6)
- D(6, -2)
Steps to try- Reflecting over the y-axis flips LEFT/RIGHT — the height stays the same.
- Switch the sign of the x-coordinate and keep the y-coordinate 6 unchanged.
- The point is 2 units left of the y-axis. Its mirror lands 2 units to the RIGHT, at the same height.
Show your work -
4Circle the letter of the best answer. Show how you know.
Which point is on the y-axis?
- A(-2, 4)
- B(0, 5)
- C(3, 3)
- D(5, 0)
Steps to try- Points on the y-axis have gone 0 units left or right — check the FIRST coordinate.
- Scan each pair's x-coordinate (the first number). Only x = 0 keeps a point on the y-axis.
- Read the first number in each pair. A point sits on the y-axis only when that number is 0.
Show your work
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.