Class 10 Mathematics – Section Formula Applications

1. What is Section Formula?

• The section formula helps us find a point that divides a line segment joining two points into a given ratio.

• The dividing point can be inside the line segment (internal division) or outside the line segment (external division).

2. Applications of the Section Formula

a) Finding the Coordinates of a Point

• Used to determine the exact position of a point dividing a line segment.

• Helps in locating intermediate points on a line between two given points.

b) Dividing a Line Segment into Equal Parts

• The formula is useful to divide a line segment into 2, 3, or more equal parts.

• For example, dividing a street or boundary line into equal sections.

c) Finding the Centroid of a Triangle (Conceptual)

• The centroid is the center point of a triangle.

• It is the point where all three medians intersect.

• Section formula helps in locating the centroid using the vertices of the triangle.

d) Application in Geometry Problems

• Determining midpoints of line segments.

• Locating points on lines that satisfy certain proportional distances.

• Helps in drawing similar or symmetrical shapes.

e) Real-Life Applications

• Dividing a road, land, or property in a given ratio.

• Locating a point between two cities proportionally.

• Determining the center of mass or balancing point in engineering.

3. Quick Tips

• Identify whether the division is internal or external.

• Always check the ratio to know how the line is divided.

• Useful in combination with distance and midpoint concepts for complete geometric analysis.

• Section formula is a powerful tool for solving many coordinate geometry problems efficiently.