Coordinate Line

Let′s draw the line `l` and will note on it the point `O`, which we take as the origin. Thereafter we must to choose the direction and the unit segment.

In this case we say, that we have coordinate line. Every naturall number or fraction corresponds to one point of line `l`. Suppose, for example, it is 3. Let′s measure from the point `O` the unit segment three times in a given direction and we will get the point `A` - and it corresponds to the number 3. Analogically, if we have the number 4.2 we will measure it from point `O` the unit segment four times in a given direction and then we measure 0.2 more of the parts of this segment and we will obtain the point `B` - it corresponds to 4.2.

If the point `M` of line `l` corresponds to number `r` then this number is called coordinate point and we write `M (r)`. So, for the points `J, A, B` we can show their coordinates: `J (1), A (3), B (4.2)`. The coordinate of point `O` is zero.

Let′s measure from the point the unit segment three times in a given direction, that is opposite of given. We will obtain the point `A`′, that is symmetric point `А`relative to the origin. The coordinate of point `A` is 3, and the coordinate of point `A`′ we write -3 and read "minus 3". Analogically, the coordinate of point `B`that is symmetric of the point `B` is number -4.2. The numbers 3 and -3, 4.2 and -4.2 are called opposite. The numbers which corresponds to the points, that are on the line in a given direction are called possitive, so 1, 3, 4.2 are possitive numbers. The numbers which corresponds to the points, that are on the line in a opposite to the given direction are called negative, so -3, -4.2 are negative numbers. Zero is considered neither positive nor negatine number.

The given direction on the coordinate line is called positive (it is usually directed to the right) and the direction opposite to the given is negative (it is directed to the left).