Find the reflection of a point `(5,-2)` in line `y=3`

Answer

To find the reflection of the point (5, -2) in the line y = 3, we can follow these steps:

### Step 1: Identify the coordinates of the point and the line
We have the point \( P(5, -2) \) and the line \( y = 3 \).

### Step 2: Determine the y-coordinate of the reflection
The formula for finding the reflection of a point \( (a, b) \) in a line \( y = m \) is given by:
\[ \text{Reflection point} = (a, 2m - b) \]
Here, \( a = 5 \), \( b = -2 \), and \( m = 3 \).

### Step 3: Substitute the values into the formula
We substitute the values into the formula:
\[ \text{Reflection point} = (5, 2 \times 3 - (-2)) \]

### Step 4: Calculate the y-coordinate
Now, we calculate the y-coordinate:
\[ 2 \times 3 = 6 \]
\[ 6 - (-2) = 6 + 2 = 8 \]

### Step 5: Write the reflection point
Thus, the reflection point is:
\[ (5, 8) \]

### Final Answer
The reflection of the point \( (5, -2) \) in the line \( y = 3 \) is \( (5, 8) \).

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