Find the reflection of a point (3,4) in line `x=-2`

Answer

To find the reflection of the point (3, 4) 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 where all points have an x-coordinate of -2.

### Step 2: Determine the distance from the point to the line
The x-coordinate of the point (3, 4) is 3. To find the distance from this point to the line x = -2, we calculate:

Distance = x-coordinate of the point - x-coordinate of the line
Distance = 3 - (-2) = 3 + 2 = 5

### Step 3: Find the x-coordinate of the reflection point
Since the reflection point will be the same distance from the line on the opposite side, we subtract this distance from the x-coordinate of the line:

Reflection x-coordinate = x-coordinate of the line - Distance
Reflection x-coordinate = -2 - 5 = -7

### Step 4: Keep the y-coordinate the same
The y-coordinate of the point (3, 4) remains unchanged during reflection. Therefore, the y-coordinate of the reflection point is still 4.

### Step 5: Write the reflection point
Combining the new x-coordinate and the unchanged y-coordinate, we find the reflection point:

Reflection point = (-7, 4)

### Final Answer
The reflection of the point (3, 4) in the line x = -2 is (-7, 4).

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