Reflecting Points in the Coordinate Plane Graph each point. Then reflect the point in the x-axis. Record the coordinates of the reflection. • A (1, 3), Reflection: • B (-2, -2) Reflection: • C (-4, 5) Reflection: • D (2, -5) Reflection: Graph each point. Then reflect the point in the y-axis. Record the coordinates of the reflection. (1, 3), Reflection: (-2, -2) Reflection: (-4, 5) Reflection: (2, -5) Reflection:
The Correct Answer and Explanation is:
Let’s work through this step-by-step.
Part 1: Reflection Across the X-Axis
When a point is reflected across the x-axis, its y-coordinate changes sign, while the x-coordinate remains the same. In formula terms, the reflection of point (x, y) over the x-axis is (x, -y).
Reflections:
- A (1, 3) → (1, -3)
- B (-2, -2) → (-2, 2)
- C (-4, 5) → (-4, -5)
- D (2, -5) → (2, 5)
Part 2: Reflection Across the Y-Axis
When a point is reflected across the y-axis, its x-coordinate changes sign, while the y-coordinate remains the same. The formula for this is: reflection of (x, y) over the y-axis is (-x, y).
Reflections:
- A (1, 3) → (-1, 3)
- B (-2, -2) → (2, -2)
- C (-4, 5) → (4, 5)
- D (2, -5) → (-2, -5)
Explanation
Reflecting points in the coordinate plane is a basic concept in geometry that helps us understand symmetry and spatial transformations. There are two main types of reflections covered in this exercise: reflection across the x-axis and reflection across the y-axis.
When reflecting across the x-axis, we are flipping the point over the horizontal axis. This means the vertical distance from the axis remains the same, but the direction changes. Mathematically, this is done by changing the sign of the y-coordinate while keeping the x-coordinate unchanged. For example, point A (1, 3) becomes (1, -3) after an x-axis reflection because it moves from 3 units above the x-axis to 3 units below.
On the other hand, reflection across the y-axis flips the point over the vertical axis. This means the horizontal distance remains the same, but again, the direction reverses. So, the x-coordinate changes sign, and the y-coordinate stays the same. For instance, point A (1, 3) reflected over the y-axis becomes (-1, 3).
Understanding these transformations helps in graphing, problem-solving, and visualizing objects in mathematics. It’s also a stepping stone for more complex topics like rotations, translations, and dilations in coordinate geometry. Reflecting points teaches symmetry, an essential concept in both mathematics and real-world applications such as engineering and design.
