Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image :
B' of B under reflection in the line AA'.

Answer

To find the image \( B' \) of point \( B \) under reflection in the line \( AA' \), we will follow these steps:

### Step 1: Identify the coordinates of points A and B
- Point \( A \) has coordinates \( (3, 4) \).
- Point \( B \) has coordinates \( (0, 2) \).

### Step 2: Determine the coordinates of point A'
- The reflection of point \( A \) across the x-axis gives us point \( A' \).
- The coordinates of \( A' \) can be found by changing the sign of the y-coordinate of \( A \).
- Therefore, \( A' \) has coordinates \( (3, -4) \).

### Step 3: Find the equation of the line \( AA' \)
- The slope of line \( AA' \) can be calculated using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 4}{3 - 3} = \frac{-8}{0} \]
- Since the slope is undefined, line \( AA' \) is a vertical line at \( x = 3 \).

### Step 4: Determine the coordinates of point B'
- To find the reflection of point \( B \) across the line \( AA' \), we need to find the horizontal distance from point \( B \) to the line \( x = 3 \).
- The x-coordinate of point \( B \) is \( 0 \), so the distance to the line \( x = 3 \) is \( 3 - 0 = 3 \).
- To find the coordinates of \( B' \), we move 3 units to the right of the line \( x = 3 \):
\[ B' = (3 + 3, y_B) = (6, 2) \]

### Final Answer
- The coordinates of the image \( B' \) of point \( B \) under reflection in the line \( AA' \) are \( (6, 2) \).

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