Chapter 1: Orienting Yourself: The Use of CoordinatesClass 9 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

This chapter introduces the two-dimensional Cartesian coordinate system, tracing its rich history from the grid-planned streets of the Sindhu-Sarasvati civilisation through Brahmagupta's formalisation of zero and negative numbers to Descartes. Two perpendicular number lines — the horizontal \(x\)-axis and the vertical \(y\)-axis — meet at the origin \(O = (0,0)\), dividing the plane into four quadrants. Every point is named by an ordered pair \((x, y)\), where \(x\) is its perpendicular distance from the \(y\)-axis and \(y\) its distance from the \(x\)-axis. Signs of the coordinates fix the quadrant: \((+,+)\), \((-,+)\), \((-,-)\) and \((+,-)\) for quadrants I to IV. Points on the \(x\)-axis have the form \((x,0)\) and points on the \(y\)-axis the form \((0,y)\). For points along a line parallel to an axis, distance is just the absolute difference of one coordinate. For any two points the chapter derives the distance formula using the Baudhayana-Pythagoras theorem: \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\). The midpoint of a segment is found by averaging coordinates.

Key terms

Extra questions & answers

Exercise Set 1.1

Think and Reflect

Think and Reflect

Exercise Set 1.2

Think and Reflect

Think and Reflect

End-of-Chapter Exercises

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