Trisection Points Tutorial Learn - how to find points that divide a line segment into three equal parts

Trisection Points Tutorial

Learn how to find points that divide a line segment into three equal parts

📚 Theory: What are Trisection Points?

Trisection points are two points that divide a line segment into three equal parts. If we have a line segment AB, the trisection points P₁ and P₂ divide it such that AP₁ = P₁P₂ = P₂B.

Section Formula:
If a point divides a line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n, then:

Point = ( m×x₂ + n×x₁ m+n , m×y₂ + n×y₁ m+n )

For Trisection Points:

• P₁ divides AB in ratio 1:2
• P₂ divides AB in ratio 2:1

🎯 Interactive Visualization

Enter Coordinates:

Point A (x₁, y₁):

Point B (x₂, y₂):

Results:

🧠 Practice Questions

Question 1:

Find the trisection points of the line segment joining A(1, 3) and B(7, -3).

First trisection point P₁:

Second trisection point P₂:

Question 2:

Find the trisection points of the line segment joining A(-2, 4) and B(4, -2).

First trisection point P₁:

Second trisection point P₂:

Question 3:

Find the trisection points of the line segment joining A(0, 0) and B(6, 9).

First trisection point P₁:

Second trisection point P₂: