A point (-4,5) is reflected in a line 𝐿1 to get the image (4,5), the equation
of the line 𝐿1 is
a) x = 4 b) y = 0 c) x = -4 d) x = 0

To determine the equation of the line \( L_1 \) where the point \((-4, 5)\) is reflected to get the image \((4, 5)\), let's analyze the situation:

1. **Reflection over a vertical line**: 
   - The \( x \)-coordinates change sign, while the \( y \)-coordinates remain the same.
   - The original point \((-4, 5)\) and its image \((4, 5)\) have the same \( y \)-coordinate. This suggests that the reflection occurred over a vertical line.

2. **Midpoint Analysis**:
   - The midpoint between the original point and its reflected image lies on the line of reflection.
   - The midpoint \( M \) of the points \((-4, 5)\) and \((4, 5)\) is calculated as:
   \[
   M = \left(\frac{-4 + 4}{2}, \frac{5 + 5}{2}\right) = (0, 5)
   \]
   - The \( x \)-coordinate of the midpoint is 0, meaning the line of reflection must be vertical and pass through \( x = 0 \).

Thus, the line \( L_1 \) where the reflection occurs is the vertical line \( x = 0 \).

The correct answer is **d) \( x = 0 \)**.

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the general method to reflect a point over a line?
2. How do you find the equation of a line given two points?
3. What happens to a point when reflected over the \( y \)-axis?
4. How does the reflection of a point over a diagonal line \( y = x \) work?
5. Can you reflect a point over a line that is not vertical or horizontal?

**Tip:** When reflecting a point over a vertical or horizontal line, only one coordinate of the point changes while the other remains the same.

Explore how to determine the equation of the line where a point (-4, 5) is reflected over a vertical line to get the image (4, 5). This detailed solution covers the concept of point reflection, analysis of coordinates, and determining the line of reflection in coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation