Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.7

Reflect Points Across Axes

Lesson 7-9 · Learn It — how the math works

Why we're learning this

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?

✱ Math Workbench

Learn It

How do you reflect a point across an axis?

A reflection is a flip of a point over a line, like a mirror image. The axis you flip over decides which coordinate changes its sign.

Picture itSee what the math looks like before you read about it

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.
Where you see this in real lifeCaptain 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.

Watch me solve itI do — read one step at a time

The problem looks like this
A coordinate grid showing (3, 2) and its reflection over the y-axis at (-3, 2).−5−5−4−4−3−3−2−2−1−11122334455 x y 0 (-3, 2)(3, 2)The dotted point is the reflection of (3, 2) over they-axis.
  1. I will reflect (3, 2) over the .
  2. The is the vertical line, so the point flips left or right. That changes the x-coordinate.
  3. The x changes sign: 3 becomes -3. The y stays the same: 2 stays 2.
  4. So the of (3, 2) over the is (-3, 2).

Watch out — mistakes students make here

  • Reflecting over the y-axis flips the x sign, not the y.
  • Don't swap the coordinates — just flip the sign of x.
  • Only the x-coordinate changes sign over the y-axis; keep y.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now let's reflect (4, -5) over the . Which coordinate changes over the x-axis?
    Check this step
    The y-coordinate.
  2. What does -5 become when it changes sign?
    Check this step
    It becomes 5.
  3. The x stays 4, so the is what point?
    Check this step
    It is (4, 5).

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot each point like (3, 5) and (-4, 2), then plot its across the given axis.

Solve: Point A is at (-3, 5). It is reflected over the to A', then A' is reflected over the to A''. What are the coordinates of A''?

My answer

Stuck? Open one hint at a time.

Hint 1

Two flips happen in a row — do them one at a time, not both at once.

Hint 2

The first flip (x-axis) changes only the y sign. Then flip THAT result over the y-axis, changing only the x sign.

Hint 3

Step 1: (-3, 5) over the x-axis — keep the -3 and flip the 5. Carry that new point into the second reflection.

Check my answer
✅ Answer: (3, -5)
Over x-axis: (-3, 5) → (-3, -5). Then over y-axis: (-3, -5) → (3, -5). Both coordinates changed sign.

Turn & TalkSay it out loud with a partner

When you reflect the point (3, 2) over the , which coordinate changes its sign and which stays the same? Why?

Try starting with:

  • The ___ coordinate changes sign.La coordenada ___ cambia de signo.
  • The ___ coordinate stays the same.La coordenada ___ se queda igual.
Use these wordsreflectionx-axisy-axisordered paircoordinate plane