The basics of the coordinate system

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The 17th-century mathematician René Descartes is considered to be the inventor of the coordinate system. One night he was lying in his bed and watched a fly sitting on the ceiling. Descartes began to wonder how he could report the location of the fly. To solve the problem, Descartes invented the coordinate system.

The Cartesian coordinate system consists of two orthogonal lines, called coordinate axes. The horizontal axis is called the x axis, whereas the vertical axis is called the y axis. The point of intersection of the two axes is called the origin.

Each point in the coordinate system has its own coordinates. The coordinates indicate the point's location inside the coordinate system. The coordinates are marked as two numbers inside brackets: [[$ ( x, y ) $]]. The order of the [[$ x $]] and [[$ y $]] coordinates in this marking is important, which is why coordinates are sometimes called ordered pairs. For example, the location of a fly in the coordinate system above is indicated as follows:

The coordinate axes divide the coordinate system into four quarters. For the points in the first quarter, both coordinates are positive. What are the signs of the coordinates in the other quarters?

Example 1

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Use coordinates to indicate the location of the following objects:

a) the lighthouse
b) the castle
c) the northern tip of the island
d) the house
e) the bear

Answers:
a) [[$(2, -4)$]]
b) [[$(1, 2)$]]
c) [[$(-1, 5)$]]
d) [[$(-4, 0)$]]
e) [[$(-3, -3)$]]

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Table of contents

1. The coordinate system

Exercises

The basics of the coordinate system

Example 1

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