Point (-5,0) and (4,0) are invariant point under reflection in the line `L_1 , ` point (0,-6) and (0,5) are invariant on reflection in the line `L_2` .
Write down the image of P(2,6) and Q (-8,-3) on reflection in `L_1` . Name the images as P' and Q' respectively.

Answer

To find the images of points P(2, 6) and Q(-8, -3) under reflection in the line L1, we follow these steps:

### Step 1: Identify the line of reflection L1
The points (-5, 0) and (4, 0) are invariant under reflection in line L1. Since these points lie on the x-axis (y = 0), we can conclude that L1 is the x-axis itself.

### Step 2: Understand the reflection process
When reflecting a point across the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign. Thus, for any point (x, y), its reflection across the x-axis will be (x, -y).

### Step 3: Reflect point P(2, 6)
Using the reflection rule:
- The x-coordinate of P remains the same: 2
- The y-coordinate of P changes sign: 6 becomes -6

So, the image of point P after reflection, denoted as P', is:
\[ P' = (2, -6) \]

### Step 4: Reflect point Q(-8, -3)
Using the same reflection rule:
- The x-coordinate of Q remains the same: -8
- The y-coordinate of Q changes sign: -3 becomes 3

So, the image of point Q after reflection, denoted as Q', is:
\[ Q' = (-8, 3) \]

### Final Answer
The images of points P and Q under reflection in line L1 are:
- P' = (2, -6)
- Q' = (-8, 3)

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