Let `A(1, 2) and B(-2,-4)` be two fixed points. A variable point P.is chosen on the straight line `y=x` such that perimeter of `DeltaPAB` is minimum. Find coordinates of P.

Explanation

To find the coordinates of point P on the line \(y = x\) such that the perimeter of triangle \(PAB\) is minimized, we can follow these steps:

### Step 1: Define the Points
Let the fixed points be:
- \(A(1, 2)\)
- \(B(-2, -4)\)

Let the variable point \(P\) on the line \(y = x\) be represented as \(P(\alpha, \alpha)\).
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