Question

Which point is the reflection of \((0,-2)\) in the \(x\)-axis? A. \((2,0)\) B. \((0,2)\) C. \((-2,0)\) D. \((0,-2)\)

Short answer

B. \( (0, 2) \)

Step-by-step solution

Understand the Concept of Reflection Over the x-axis

When a point \( (x, y) \) is reflected over the x-axis, its y-coordinate changes sign while the x-coordinate stays the same. In other words, the reflected point is \( (x, -y) \).

Identify the Original Coordinates

The original point given is \( (0, -2) \).

Apply the Reflection Rule

According to the reflection rule, the point \( (0, -2) \) reflected over the x-axis will be \( (0, -(-2)) \), which simplifies to \( (0, 2) \).

Determine the Correct Answer Choice

The reflected point is \( (0, 2) \). Among the given options, choice B \( (0, 2) \) is the correct answer.

Key concepts

Coordinate Plane

The coordinate plane, also known as the Cartesian plane, is a two-dimensional surface defined by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). It allows us to locate points using ordered pairs \((x, y)\). Each ordered pair represents a specific point on the plane. The first number in the pair corresponds to the x-coordinate, indicating the position along the horizontal axis. The second number is the y-coordinate, representing the position along the vertical axis.
For example, the point \((0, -2)\) is located on the y-axis, 2 units below the origin (0,0). Understanding how to read and plot points on the coordinate plane is fundamental in geometry, as it forms the basis for reflecting points and other transformations.

x-axis Reflections

A reflection in geometry is a type of transformation that 'flips' a point or shape over a line, creating a mirror image. When reflecting a point over the x-axis, the x-coordinate remains unchanged, and the y-coordinate changes sign. This rule can be expressed as changing point \((x, y)\) to \((x, -y)\).
For example, if you reflect the point \((0, -2)\) over the x-axis, the x-coordinate stays at 0, and the y-coordinate becomes the opposite: \(-(-2) = 2\). Hence, the new reflected point is \((0, 2)\).
Reflecting points in this manner helps in understanding symmetrical properties and is a critical skill for solving various geometric problems.

GED Test Preparation

Preparation for the General Educational Development (GED) test can be challenging, especially in subjects like math and geometry. Understanding reflections on the coordinate plane is a frequent topic tested on the GED.
Here are some tips to help with your preparation:

• Practice Regularly: Consistent practice with geometric transformations helps solidify concepts. Reflect various points and shapes over the x-axis and other lines of symmetry to become more comfortable with the process.
• Use Visual Aids: Drawing graphs and sketches can significantly aid in understanding and visualizing reflections and other transformations. Use graph paper to plot points accurately.
• Memorize Key Rules: Remember essential rules, such as reflection over the x-axis changes \((x, y)\) to \((x, -y)\). These basic rules are often the foundation of many GED geometry questions.
• Tackle Practice Tests: Completing sample GED math tests helps familiarize yourself with question patterns and difficulty levels. It also highlights areas where you need improvement.

With these strategies, you can build confidence and improve your performance in the GED geometry section.