What is the Section Formula for Internal Division? | Don't Memorise

TL;DR

The section formula allows us to find the coordinates of a point on a line segment given the ratio of division and coordinates of the endpoints.

Transcript

consider the line segment ab and a point P somewhere in between the end points here Point p is slightly closer to a doesn't matter where it lies on the segment a point will always divide a segment into two parts in this case the point P divides the segment AB into two parts a p and PB this is called the internal division of a line segment the point... Read More

Key Insights

• ➗ Internal division of a line segment occurs when a point divides it into two parts, with one part between the endpoints.
• 🥳 The section formula allows for finding the coordinates of the point of internal division using the ratio and endpoint coordinates.
• 🥳 The section formula involves multiplying the coordinates of the endpoints with the ratio and dividing the sums by the sum of the ratio.
• 😥 External division is possible when a point divides a line segment from outside, creating two parts between the point and the endpoints.
• 😥 The section formula applies to both internal and external division, providing coordinates for the dividing point.
• 👈 The X-coordinate of the dividing point is obtained by applying the section formula to the X-coordinates of the endpoints.
• 🇾🇪 The Y-coordinate of the dividing point is obtained by applying the section formula to the Y-coordinates of the endpoints.

Questions & Answers

Q: What is internal division in a line segment?

Internal division refers to a point dividing a line segment into two parts, with one part being closer to the initial endpoint.

Q: How can the section formula be used to find the coordinates of a point?

The section formula involves multiplying the coordinates of each endpoint by the ratio of division and dividing the sums by the sum of the ratio. This gives the coordinates of the point.

Q: Can a point also divide a line externally?

Yes, a point can divide a line externally. In this case, the point lies outside the segment and creates two parts: one from the initial endpoint to the point and the other from the point to the final endpoint.

Q: What information is needed to use the section formula?

To use the section formula, you need the ratio in which the point divides the line segment and the coordinates of the endpoints.

Summary & Key Takeaways

• A point on a line segment divides it into two parts, known as internal division.

• The section formula provides a way to find the coordinates of the point that divides the line segment internally.

• The formula involves multiplying the coordinates of the endpoints with the ratio of division and dividing the sums by the sum of the ratio.