Lesson 1 of 10 · 6 min

Why a point needs three numbers

NCERT §11.1

Kavya's drone club flies on the school ground. The launch pad is marked O. The club's app shows the drone's spot on a ground map: 3 m towards the gate and 4 m towards the pavilion. Does that tell you where the drone is?

The story this chapter follows: The drone club on the school ground

Imagine Kavya's school drone club flying from a launch pad on the school ground. The pad is the origin, x runs towards the gate, y towards the pavilion and z straight up, with a rain-water tank sunk below the ground. Every hover point, shadow, beacon and formation in this chapter is a point with three coordinates.

The lesson in notes

In short

On a flat sheet two perpendicular lines and two numbers are enough to pin down any point. Real objects are not confined to a sheet: a thrown ball or an aircraft in flight moves through space.

Take the lowest tip of a bulb hanging in a room. Its distances from two walls that meet at a corner fix only the spot on the floor straight below it; its height above the floor is still unknown.

So a point in space needs three numbers: its perpendicular distances from three mutually perpendicular planes, such as the floor and two adjacent walls. These three numbers are its coordinates with respect to those planes.

Every idea in this chapter is the plane geometry of the earlier chapters with one more coordinate added and handled the same way.