In what ratio, the line joining `(1, 1)`and `(5, 7)`is divided by the line `x+y=4`?

Explanation

To solve the problem of finding the ratio in which the line joining the points \( A(1, 1) \) and \( B(5, 7) \) is divided by the line \( x + y = 4 \), we can follow these steps:

### Step 1: Identify the Points and the Line
Let \( A(1, 1) \) and \( B(5, 7) \) be the points. The line \( x + y = 4 \) will intersect the line segment \( AB \) at some point \( M \).

### Step 2: Use the Section Formula
Assume that point \( M \) divides the line segment \( AB \) in the ratio \( \lambda : 1 \). According to the section formula, the coordinates of point \( M \) can be expressed as:

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