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निर्देशांक ज्यामिति (Coordinate Geometry) Notes

Home / Class Notes / Class 10 / Math / निर्देशांक ज्यामिति (Coordinate Geometry)
✓ Free notes Class 10 Math 0 study files

About these notes

Class 10 Math CBSE and Bihar Board निर्देशांक ज्यामिति (Coordinate Geometry) is presented as clear notes with key definitions, formulae, diagrams and worked examples for quick revision. Main sub-topics: Cartesian plane and coordinates, distance formula, midpoint and section formula (internal/external), slope and equation of a line (two-point, slope-intercept), conditions for parallel/perpendicular, area of triangle using coordinates and collinearity. Ideal for Class 10 students preparing for school and board exams; practise using chapter test and board-pattern mock tests on Merit Spring ROH. Also useful for quick revision, important questions, MCQ and question answer practice.

Key points you will learn

  • Class 10 Math CBSE and Bihar Board निर्देशांक ज्यामिति (Coordinate Geometry) notes
  • Distance formula: √[(x2−x1)²+(y2−y1)²]
  • Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
  • Section formula (internal, AP:PB = m:n): ( (mx2+nx1)/(m+n), (my2+ny1)/(m+n) )
  • Slope m = (y2−y1)/(x2−x1); line forms: y = mx + c and (y−y1) = m(x−x1)
  • Area of triangle: 1/2 |x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|; zero ⇒ collinear
  • Condition for parallel/perpendicular: m1 = m2 and m1·m2 = −1
  • Distance from point (x0,y0) to line ax+by+c=0: |ax0+by0+c|/√(a²+b²)

What is inside this chapter

Notes for this chapter will be added soon.

Questions students ask

What are the main formulas in Class 10 निर्देशांक ज्यामिति?

The main formulas are distance √[(x2−x1)²+(y2−y1)²], midpoint ((x1+x2)/2,(y1+y2)/2), section formula for ratio m:n, slope m=(y2−y1)/(x2−x1), line equations y=mx+c and two-point form, area of triangle using determinants.

How to use the section formula to divide a line in given ratio?

To find coordinates of a point dividing AB in ratio m:n (internal), use ((mx2+nx1)/(m+n), (my2+ny1)/(m+n)). Swap m and n or change sign for external division and always check order of endpoints.

Where can I practise Class 10 निर्देशांक ज्यामिति MCQ and chapter test?

Merit Spring ROH provides chapter test and board-pattern mock tests site-wide for practice and instant scoring; use those to check time-management and accuracy after revising notes and important questions on the chapter.

How do I find area of a triangle using coordinates and test collinearity?

Use area = 1/2 |x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|; if the result is zero, the three points are collinear. This formula also helps solve many exam-style questions efficiently.

← Previous chapter त्रिभुज (Triangles)

More Math chapters

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

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