Section Formula

Section Formula:

Definition:

The Section Formula is used to find the coordinates of a point that divides a line segment joining two given points in a specific ratio.

Formula:

Let P(x,y) be the point dividing the line segment joining A(x1,y1) and B(x2,y2) in the ratio m:n. The coordinates of P are given by:

x=mx2+nx1m+n y=my2+ny1m+n

Example:

Consider two points A(3, 5) and B(7, 9). Find the coordinates of a point P that divides AB in the ratio 2:3.

Steps to Solve:

  1. Identify Coordinates:

    • Point A: x1=3,y1=5
    • Point B: x2=7,y2=9
    • Ratio: m=2,n=3
  2. Apply Section Formula: x=mx2+nx1m+n y=my2+ny1m+n

  3. Substitute Values: x=2×7+3×32+3 y=2×9+3×52+3

  4. Perform Arithmetic: x=14+95=235=4.6 y=18+155=335=6.6

  5. Final Answer: The coordinates of point P, which divides the line segment AB in the ratio 2:3, are approximately (4.6, 6.6).

Interpretation:

Using the Section Formula, we've found the coordinates of point P that divides the line segment AB in the ratio 2:3. These coordinates represent the location of point P along the line segment joining points A and B in the given ratio.