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Section Formula — Revision Notes

ICSE · Class 10 · Mathematics

Section Formula revision notes for ICSE Class 10 Mathematics: 4 topics in quick points. Part of the ICSE Class 10 Mathematics syllabus.

33 questions20 flashcards9 formulas & key relations5 concepts

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A diagram illustrating the section formula for internal division, showing a point P dividing a line segment AB in a given ratio m:n on a Cartesian plane, with coordinates and the formula.
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Key Topics to Revise

1

1. Section Formula: Internal Division

  • Point P divides line segment AB internally in the ratio m:n, written as PA:PB = m:n.
  • The coordinates of P are found using the section formula for internal division.
  • The order in the formula is important: m is multiplied with the second point and n is multiplied with the first point.
2

2. Proof Idea for the Section Formula

  • Perpendiculars are drawn to the X-axis in the proof: AL, BN, PM, AQ and PR are used to form similar triangles.
  • Triangle AQP and triangle PRB are similar.
  • From similarity, the ratio relation is obtained.
3

3. Mid-point Formula

  • The midpoint is the point exactly halfway between two points.
  • The midpoint formula is obtained by putting m=n in the section formula.
  • If a point divides a segment in the ratio 1:1, it is the midpoint.
4

4. Centroid of a Triangle

  • The centroid of a triangle is the point of intersection of its medians.
  • For triangle ABC with vertices A(x1,y1), B(x2,y2), and C(x3,y3), the centroid is found using the coordinate formula.
  • D is the midpoint of BC.

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Full Notes

Key Concepts

If point P lies onIf A(x1Perpendiculars are drawn to the xThe midpoint of AB has coordinatesThe centroid is the point

Frequently Asked Questions

What are the important topics in Section Formula for ICSE Class 10 Mathematics?
Key topics in Section Formula include Section Formula: Internal Division, Proof Idea for the Section Formula, Mid-point Formula, Centroid of a Triangle. Study these first, then practise questions on each for the ICSE Class 10 board exam.
How should I revise Section Formula for the ICSE Class 10 board exam?
Learn the core ideas first, then work through the 33 practice questions on Section Formula. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All ICSE Class 10 Mathematics Revision Notes

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