Revision Notes: Class 10 Maths Chapter 7 Coordinate Geometry

Free Coordinate Geometry Class 10 notes PDF-style revision — every formula from Chapter 7 (distance formula, section formula, area of a triangle) in one place.

Last Updated: October 24, 2026

Common Mistakes Students Make in Coordinate Geometry

A fast, one-glance recap of Class 10 Maths Chapter 7 (Coordinate Geometry) — for full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 7 notes are ideal for quick revision just before exams.

Why This Chapter Matters

Coordinate Geometry is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

Revision Notes: Coordinate Geometry

• Distance formula: d=√((x₂-x₁)²+(y₂-y₁)²)
• Distance from origin: √(x²+y²)
• Section formula (ratio m:n, internal): ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
• Midpoint formula (m=n): ((x₁+x₂)/2, (y₁+y₂)/2)
• Collinearity test: three points are collinear if the area of the triangle they form is 0
• Area of a triangle: ½|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
• Locus equidistant from two points: the perpendicular bisector of the segment joining them
• Type of quadrilateral: use all 4 sides + both diagonals together (equal sides + equal diagonals = square; equal sides only = rhombus; opposite sides equal = parallelogram)
• 2023 rationalisation: only Ex 7.1 (Distance Formula) and Ex 7.2 (Section Formula) remain as numbered exercises — the old Ex 7.3 (Area of a Triangle) and Ex 7.4 (Optional) were removed, though the area formula itself remains useful (see Extra Questions)

Two points plotted on the Cartesian plane, as used in distance and section-formula problems.

See also: Extra Questions (HOTS) | Formulas Handbook

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Frequently Asked Questions

What is the section formula used for in Coordinate Geometry?
It is used to find the coordinates of a point that divides the line segment joining two given points in a given ratio (internally) — a very frequently tested formula in this chapter.

How is the distance formula derived, and what is it used for?
It comes directly from applying the Pythagorean theorem to the horizontal and vertical differences between two points’ coordinates; it is used to find the distance between any two points in the plane, and by extension to check whether three points are collinear or form a specific type of triangle/quadrilateral.

What to Revise First (and Last) in This Chapter

Written by Satish

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