Find the reflection of the point P(-1,3) in the line x = 2

Answer

To find the reflection of the point P(-1, 3) in the line x = 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Point and Line**:
- We have the point P with coordinates (-1, 3).
- The line of reflection is given by the equation x = 2.

2. **Understand the Geometry**:
- The line x = 2 is a vertical line that runs parallel to the y-axis.
- The reflection of a point across a vertical line will have the same y-coordinate but a different x-coordinate.

3. **Calculate the Distance from the Point to the Line**:
- The x-coordinate of point P is -1.
- The x-coordinate of the line is 2.
- The distance from point P to the line x = 2 is calculated as:
\[ \text{Distance} = |2 - (-1)| = |2 + 1| = 3 \text{ units} \]

4. **Find the x-coordinate of the Reflected Point**:
- Since the distance from P to the line is 3 units, we need to move 3 units to the right of the line x = 2 to find the reflected point.
- Therefore, the x-coordinate of the reflected point P' will be:
\[ 2 + 3 = 5 \]

5. **Keep the y-coordinate the Same**:
- The y-coordinate of the reflected point P' remains the same as that of point P, which is 3.

6. **Write the Coordinates of the Reflected Point**:
- Thus, the coordinates of the reflected point P' are (5, 3).

### Final Answer:
The reflection of the point P(-1, 3) in the line x = 2 is P'(5, 3).

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