Unit 9 · Standard 6.NS.6b
Reflect Points Across Axes
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
(3, 2) reflected over the y-axis becomes (-3, 2) — x changes sign, y stays
Reflection
A flipped image of a point on the other side of a line, the same distance away.
(4, 3) → (4, -3): the y flips from +3 to -3, like folding the paper along the horizontal line
x-axis
The line that goes across the grid. Flipping over it changes the y sign.
(4, 3) → (-4, 3): the x flips from +4 to -4, like folding the paper along the vertical line
y-axis
The line that goes up the grid. Flipping over it changes the x sign.
A butterfly's wings are symmetric — fold it down the middle and both sides match
Symmetry
When a shape looks the same on both sides of a line.
..., -3, -2, -1, 0, 1, 2, 3, ...
Integer
Whole numbers and their opposites, like -2, -1, 0, 1, 2.
Key Ideas & Notes
- 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).
- Plot each original point and then plot its reflection across the given axis.
Think About It
- When (2, 4) reflects over the x-axis to (2, -4), which coordinate changed?
- When (5, 3) reflects over the y-axis to (-5, 3), which coordinate changed?
- What stays the same in each reflection?
My Notes
Guided Examples
Example 1
What is the reflection of (4, -3) over the x-axis?
Solution: Reflecting over the x-axis changes the sign of the y-coordinate. The x stays the same (4), and the y changes from -3 to 3. The answer is (4, 3).
Answer: B. (4, 3)
Example 2
What is the reflection of (-2, 6) over the y-axis?
Solution: Reflecting over the y-axis changes the sign of the x-coordinate. x goes from -2 to 2, and y stays 6. The answer is (2, 6).
Answer: A. (2, 6)
Example 3
Which point is on the y-axis?
Solution: Points on the y-axis have x-coordinate = 0. (0, 5) is on the y-axis.
Answer: A. (0, 5)
Write About the Math The Writing Revolution
I can explain my work using the words reflection, x-axis, y-axis, and symmetry.
1. Kernel Sentence subject + verb
Model: Reflection is a flipped image of a point on the other side of a line, the same distance away.Reflexión es una imagen volteada de un punto al otro lado de una línea, a la misma distancia.
Write a kernel sentence about reflection. Use a subject and a verb.Escribe una oración base sobre reflexión. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Reflection matters in mathReflexión importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Reflection matters in math because ___.Reflexión importa en matemáticas porque ___.
Reflection matters in math, but ___.Reflexión importa en matemáticas, pero ___.
Reflection matters in math, so ___.Reflexión importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about reflection.Di un hecho verdadero sobre reflection.
Reflection ___.
Ask a question about reflection.Haz una pregunta sobre reflection.
How does ___ ?¿Cómo ___ ?
Show excitement about reflection.Muestra entusiasmo sobre reflection.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with reflection.Dile a un compañero qué hacer con reflection.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
When I reflect across the ___ axis, ___ changes.Al reflejar sobre el eje ___, cambia ___.
The new point is ___.El punto nuevo es ___.
I see reflections in ___.Veo reflexiones en ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which point is on the y-axis?
- (0, 5)
- (5, 0)
- (3, 3)
- (-2, 4)
2. Point A is at (-3, 5). It is reflected over the x-axis to A', then A' is reflected over the y-axis to A''. What are the coordinates of A''?
- (3, -5)
- (-3, -5)
- (3, 5)
- (-3, 5)
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A triangle has vertices at A(1, 2), B(4, 2), and C(4, 6). If you reflect the entire triangle over the y-axis, what are the new vertices? What do you notice about the size and shape of the reflected triangle compared to the original?
Sentence starter: The reflected vertices are A'(___), B'(___), C'(___). I found each by ___. The reflected triangle is ___ compared to the original because reflections ___.
Reflect — Exit Ticket
What is the reflection of (-5, 2) over the y-axis?
- (-5, -2)
- (5, -2)
- (5, 2)
- (2, -5)
Answer Key & Teacher Guide
- Try It 1: A. (0, 5) — Points on the y-axis have x-coordinate = 0. (0, 5) is on the y-axis.
- Try It 2: A. (3, -5) — Over x-axis: (-3, 5) → (-3, -5). Then over y-axis: (-3, -5) → (3, -5). Both coordinates changed sign.
- Exit Ticket: C. (5, 2) — Reflecting over the y-axis changes the sign of the x-coordinate. x goes from -5 to 5, and y stays 2. The reflection is (5, 2).
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Reflection is a flipped image of a point on the other side of a line, the same distance away.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).