Point P (h,k) divides a line segment between the exes in the ratio `1:2` Find the lengths (intercepts) on the axes made by this segment. Also find the area of triangle formed by the line segment and the axes.

Explanation

To solve the problem step by step, we will find the lengths of the intercepts on the axes made by the line segment that point P (h, k) divides in the ratio 1:2, and then we will calculate the area of the triangle formed by the line segment and the axes.

### Step 1: Understand the problem
We have a point P(h, k) that divides the line segment between the x-axis and y-axis in the ratio 1:2. We need to find the intercepts on the axes and the area of the triangle formed by these intercepts.

### Step 2: Define the points of intercepts
Let:
- Point A be the intercept on the x-axis, which has coordinates (x, 0).
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