The point (-5,0) on reflection in a line is mappped as (5,0) and the point (-2,-6) on reflection in the same line is mapped as (2,-6)
(a) Name the line of reflection. (b) Write the co-ordinates of the image of (5,-8) in the line obtained in (a).

Answer

To solve the problem step by step, we will first identify the line of reflection and then find the coordinates of the image of the point (5, -8) after reflection across that line.

### Step 1: Identify the line of reflection
Given the points:
- Point A: (-5, 0) maps to A': (5, 0)
- Point B: (-2, -6) maps to B': (2, -6)

To find the line of reflection, we observe how the points are reflected:
- The x-coordinates of points A and A' are opposites, indicating that the line of reflection is the y-axis (x = 0).
- Similarly, for points B and B', the x-coordinates are also opposites, confirming that the line of reflection is indeed the y-axis.

Thus, the line of reflection is:
**x = 0 (the y-axis)**

### Step 2: Find the coordinates of the image of (5, -8)
Now, we need to find the image of the point (5, -8) when reflected across the line x = 0.

1. The point (5, -8) is located 5 units to the right of the y-axis.
2. When reflected across the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same.

Therefore, the image of the point (5, -8) will be:
- The x-coordinate becomes -5.
- The y-coordinate remains -8.

Thus, the coordinates of the image are:
**(-5, -8)**

### Final Answers:
(a) The line of reflection is **x = 0** (the y-axis).
(b) The coordinates of the image of (5, -8) are **(-5, -8)**.