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Two numbers can name one exact spot on a page. This chapter shows you how.

This is Chapter 1 in your NCERT Maths book. It is called Orienting Yourself: The Use of Coordinates.

A grid has two number lines. Each one is an axis. A point's two numbers are x and y. A circle's radius is r.

What you will learn

• One point, one pair. Two numbers, in order, name one spot.
• Four regions. The two signs decide which one.
• A shared coordinate. One subtraction gives the distance.
• The distance. Two points and a helper point make a right triangle.
• The midpoint. Average each coordinate on its own: add, then halve.
• In a line, or not. An exact arithmetic check.
• A square corner. A right angle: three squared sides, one addition.
• Naming a shape. Sides, diagonals (lines joining opposite corners), midpoints.
• A mirror on an axis. One sign flips. Lengths stay.
• Against a circle. Compare x² + y² with r².

Need a quick recap?

These earlier lessons help. Open any you are unsure about.

• The two smaller squares add up to the biggest one.
• Finding the long side — square, add, then take the square root.
• Testing a triangle without a protractor — three lengths test the corner.
• Five shape names — each needs its own checks.
• When joining dots is allowed — a graph's scale has an order.
• A number, not a broken number. A minus sign names which side of zero.