If sum of the perpendicular distances of a variable point `P (x , y)`from the lines `x + y =5 `and `3x - 2y +7 = 0`is always 10. Show that P must move on a line.

Explanation

To solve the problem, we need to show that the point \( P(x, y) \) moves along a straight line given that the sum of the perpendicular distances from two lines is always 10. Let's break this down step by step.

### Step 1: Identify the equations of the lines
The two lines given are:
1. \( x + y = 5 \) (let's call this Line 1)
2. \( 3x - 2y + 7 = 0 \) (let's call this Line 2)

### Step 2: Write the equations in standard form
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