Class 10 Maths — Chapter 7: Coordinate Geometry
Chapter 7: Coordinate Geometry is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 6 topics including Review of Cartesian Coordinate System, The Distance Formula, Distance of a Point from the Origin. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Review of Cartesian Coordinate Systemcoordinateabscissaordinatex-axisy-axis
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▸The Distance FormulaCore conceptdistance formulaPythagoras theoremcoordinatesdistance between two points
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▸Distance of a Point from the OriginCore conceptorigindistance from origin√(x² + y²)special case
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▸Application: Identifying Types of TrianglesCore concepttriangleisoscelesequilateralright-angled triangleconverse of Pythagoras
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▸Application: Verifying Collinearity of Pointscollinearstraight linetriangle inequalitysum of distances
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▸Application: Identifying Types of Quadrilateralsquadrilateralsquarerhombusrectanglediagonals
Chapter Summary
Understanding the foundational concepts of the coordinate plane, including locating points using ordered pairs (x, y), and identifying the x-coordinate (abscissa) and y-coordinate (ordinate). This includes knowing the coordinate forms for points on the x-axis (x, 0) and y-axis (0, y).
Deriving and applying the formula to calculate the distance between any two points P(x₁, y₁) and Q(x₂, y₂). The formula is PQ = √((x₂ - x₁)² + (y₂ - y₁)²), derived from the Pythagorean theorem.
Applying a special case of the distance formula to find the distance of a point P(x, y) from the origin O(0, 0). The simplified formula is OP = √(x² + y²).
Using the distance formula to find the lengths of the three sides of a triangle and classifying it as scalene, isosceles, or equilateral. Students must also be able to use the converse of the Pythagorean theorem to check if it is a right-angled triangle.
Using the distance formula to determine if three points lie on the same straight line. This is confirmed if the sum of the distances of any two pairs of points equals the distance of the third pair (e.g., AB + BC = AC).
Applying the distance formula to find the lengths of all four sides and both diagonals of a quadrilateral to classify it. For example, a square has four equal sides and equal diagonals, while a rhombus has four equal sides but unequal diagonals.
Practice Questions from this Chapter
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- Explain real-world coordinate uses? Get Solution →
- Graph my name on axes? Get Solution →
- Calculate distance between faraway cities? Get Solution →
- What is another name for the x-coordinate of a point? Get Solution →
- What is the general form of the coordinates for any point on the y-axis? Get Solution →
- Which mathematical theorem is the foundation for the distance formula in coordinate geometry? Get Solution →
- What is another name for the y-coordinate of a point? Get Solution →
- A graphical representation of a linear equation in two variables, `ax + by + c = 0`, is a what? Get Solution →
Did you know?
- 💡 René Descartes developed coordinate geometry by watching a fly on his ceiling.
- 💡 GPS systems use coordinate geometry to locate any spot on Earth precisely.
- 💡 Astronomers use celestial coordinates to accurately map the positions of stars.
- 💡 Computer graphics use coordinates to draw all the complex shapes you see on screens.
- 💡 Mathematicians can describe objects using coordinates in over ten dimensions.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 6 key topics: Review of Cartesian Coordinate System, The Distance Formula, Distance of a Point from the Origin, Application: Identifying Types of Triangles, Application: Verifying Collinearity of Points, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 7: Coordinate Geometry important for board exams?
Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 10?
Yes. BrainWeave's free Spark plan gives generous daily messages — enough for regular homework. Premium features unlock when you bring your own free Google Gemini API key.
Can I use voice chat for this chapter?
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