Explanation of the Process:

The given equation p/q = r/s = p-r/ q - s is referred to as the mid-point theorem in Mathematics.

Mid-Point Theorem:

The mid-point theorem is a theorem that states that if a line segment joins two points on a triangle, then the line segment is parallel to the third side and is equal to half of it.

Application of Mid-Point Theorem:

The given equation can be simplified using the mid-point theorem in the following way:

- Let us assume that the line segment joining two points on the triangle is the line segment joining the midpoints of two sides of the triangle.

- Then, the third side of the triangle is equal to the sum of the line segments joining the midpoints of the other two sides of the triangle.

- In other words, p/q = r/s = p-r/ q - s means that the line segment joining the midpoints of the sides of the triangle is parallel to the third side and equal to half of it.

Significance of Mid-Point Theorem:

The mid-point theorem has several applications in Mathematics, especially in geometry. Some of its significant applications are:

- It helps in finding the distance between two points on a line segment.

- It is used in proving various theorems in Geometry.

- It helps in solving problems related to triangles, such as finding the length of the median and the altitude.

- It is used in constructing various geometric figures.

Conclusion:

The mid-point theorem is a fundamental concept in Mathematics, and it has several applications in geometry. The given equation, p/q = r/s = p-r/ q - s, is an example of the mid-point theorem, which states that the line segment joining two points on a triangle is parallel to the third side and equal to half of it.