What is the reflection of the point (-3,1) in the line x=-2

Options

A. `(-1,1)`
B. `(-3,-5)`
C. `(1,1)`
D. `(-3,5)`

Answer

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

### Step 1: Identify the line of reflection
The line of reflection is given as x = -2. This is a vertical line that runs through all points where the x-coordinate is -2.

### Step 2: Determine the distance from the point to the line
The point we are reflecting is (-3, 1). To find the distance from this point to the line x = -2, we calculate the difference in the x-coordinates:
- Distance = |-3 - (-2)| = |-3 + 2| = |-1| = 1

### Step 3: Calculate the x-coordinate of the reflected point
To find the x-coordinate of the reflected point, we need to move the same distance (1 unit) from the line x = -2 to the opposite side. Since the original point (-3, 1) is to the left of the line, we will move to the right:
- New x-coordinate = -2 + 1 = -1

### Step 4: Keep the y-coordinate the same
The y-coordinate of the point does not change when reflecting over a vertical line. Therefore, the y-coordinate remains the same:
- y-coordinate = 1

### Step 5: Write the coordinates of the reflected point
Combining the new x-coordinate and the unchanged y-coordinate, the coordinates of the reflected point are:
- Reflected point = (-1, 1)

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

---