How two number lines let you describe any location exactly: plot points, name quadrants, and find the distance between two points.
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concepts · 3
Plot points using (x, y), and work out which quadrant each one is in.
Work out the distance formula from Pythagoras, and use it to measure slanted lines.
Use plotting and distance together on bigger problems: points in a line, squares and midpoints.
Reiaan's room laid out on a grid of pins and threads.
A simple grid of horizontal and vertical distances allows us to pinpoint the exact location of any object.
How Reiaan finds his way around a room he cannot see, using a grid.
Imagine moving to a new house and needing to navigate your room without being able to see. How would you know exactly where the wardrobe or the bed is?
By the end of this chapter, you will be able to solve problems like locating exact positions on a map using only pairs of numbers.
Tick what you already know about number lines.
A few questions on number lines before you move to two dimensions.
What is the total distance between the numbers and on a standard number line?
Concept: grid-based-thinking
Grid streets in the Sindhu-Sarasvatī cities, and Brahmagupta's work on zero and negative numbers.
Grid-based thinking has deep roots! Thousands of years ago, the Sindhu-Sarasvatī Civilisation built city streets with striking precision in North-South and East-West directions, exactly 10 meters apart. Much later, Brahmagupta formalised zero and negative numbers, laying the foundation for the modern coordinate planes we use today.