Coordinate Geometry Notes

✓ Free notes Class 10 Math 1 study file

About these notes

Class 10 Math Coordinate Geometry notes give step-by-step formulas and worked techniques for distance, midpoint, section formula and triangle area so you can practise important questions, MCQ and prepare for chapter tests. Main sub-topics: Cartesian plane and plotting points, distance formula, midpoint formula, section (internal and external) formula, triangle area by 1/2 × base × height and the determinant method, vertical/horizontal distances |Δx| and |Δy|, and the collinearity (area = 0) check. Useful for Class 10 students preparing for board exams, chapter tests and mock tests.

Key points you will learn

Class 10 Math Coordinate Geometry notes: distance formula, midpoint, section (internal/external), triangle area
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
Section formula (internal) for ratio m:n → ((m x2 + n x1)/(m + n), (m y2 + n y1)/(m + n))
Section formula (external) uses (m x2 - n x1)/(m - n) and (m y2 - n y1)/(m - n)
Triangle area (determinant): 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Vertical/horizontal distances are |Δx| or |Δy|; always sketch points to avoid sign/quadrant mistakes
Collinearity test: three points are collinear if triangle area = 0 (use determinant)

What is inside this chapter

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Coordinate Geometry

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Questions students ask

Where to find Class 10 Math Coordinate Geometry notes and important questions?

Find Class 10 Math Coordinate Geometry notes and important questions on msroh.in's Coordinate Geometry page. The page highlights core formulas, techniques and gives practice direction; use the site’s chapter tests and mock tests plus MCQ practice for fast revision and exam tips.

How to find the distance between (0,0) and (6,8)?

Distance = 10 units. Use the distance formula: d = √((6-0)² + (8-0)²) = √(36 + 64) = √100 = 10; always plot points first to check signs and quadrant placement.

Find the coordinates of the point which divides the line segment joining (1,-2) and (4,7) in the ratio 2:1 internally.

(3, 4). Use the internal section formula: x = (m x2 + n x1)/(m + n), y = (m y2 + n y1)/(m + n). Here x = (2·4 +1·1)/3 =3, y = (2·7 +1·(-2))/3 =4.

How to find the area of triangle with vertices (0,0), (4,0) and (4,3)?

Area = 6 square units. Use 1/2 × base × height: base = 4 (along x-axis), height = 3, so area = 1/2 × 4 × 3 = 6. The determinant formula gives the same result.

What is the midpoint of the line segment joining (0,0) and (4,6)?

(2, 3). Apply midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((0+4)/2, (0+6)/2). Plot the midpoint to verify it lies halfway between the endpoints.

More Math chapters

Real Numbers Polynomials Pair of Linear Equations in Two Variables Quadratic Equations Arithmetic Progressions Triangles All chapters →

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