Reflect Points Across Axes
Name Period
Objectives / Objetivos
Content Objective: I can reflect points across the x-axis and y-axis on the coordinate plane.
Language Objective: I can explain my work using the words reflection, x-axis, y-axis, and symmetry.
Key Idea / Idea clave
Reflections Across Axes. Formula: Reflect over x-axis: (x, y) → (x, −y) | Reflect over y-axis: (x, y) → (−x, y). 1. Reflection across x-axis (horizontal line): y-coordinate changes sign, x stays same. 2. Reflection across y-axis (vertical line): x-coordinate changes sign, y stays same. 3. Both coordinates change sign when reflecting across both axes: (−x, −y)
I Notice / Observo
- 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?
I Wonder / Me pregunto
- What happens if you reflect a point over BOTH axes?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Reflect Points Across Axes Reflejar puntos sobre los ejes | Flip a point across an axis so it stays the same perpendicular distance from that axis. Voltear un punto sobre un eje para que quede a la misma distancia perpendicular de ese eje. |
| Reflection Reflexión | A flipped, mirror image across a line. Una imagen reflejada al otro lado de una línea. |
| x-axis Eje x | The line that goes across the grid. Flipping over it changes the y sign. La línea que va de lado en la cuadrícula. Voltear sobre ella cambia el signo de y. |
| y-axis Eje y | The line that goes up the grid. Flipping over it changes the x sign. La línea que va hacia arriba en la cuadrícula. Voltear sobre ella cambia el signo de x. |
| Symmetry Simetría | When a shape looks the same on both sides of a line. Cuando una figura se ve igual a ambos lados de una línea. |
| Integer Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. Números enteros y sus opuestos, como -2, -1, 0, 1, 2. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the reflection of (4, -3) over the x-axis?
- A (-4, -3)
- B (-4, 3)
- C (3, -4)
- D (4, 3)
Answer:
2. Plot (1, 4). Find and plot its reflection across the x-axis, its reflection across the y-axis, and its reflection across both axes. Start from the original point each time.
- Original: (1, 4)
- Across x-axis: Reflect the original point across the x-axis.
- Across y-axis: Reflect the original point across the y-axis.
- Across both axes: Reflect the original point across both axes.
3. Find the reflection of each point over the given axis.
Complete each empty cell. Show your reasoning below.
| Original Point | Axis | Reflected Point |
|---|---|---|
| (3, -7) | x-axis | |
| (-5, 2) | y-axis | |
| (8, -1) | x-axis | |
| (-4, -6) | y-axis | |
| (0, 9) | x-axis | |
| (-3, 0) | y-axis |
4. Find the Reflection Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: