# How to find the length of a segment on the coordinate axis ?

- line
- ability to carry out elementary arithmetic

segment - the locus of points lying on the same line and prisoners within its ends.End of the segment are the points.The segment is a closed set, therefore, it is possible to determine its size.Measure the size of the segment is its length.Calculate the length of the segment can be accurately and about.For a rough calculation it is necessary to use the means at hand.How to find the length of the segment using a ruler?It is enough to make the start line to the top of the segment and look at a segment of the figure ends.This will be its length.But keep in mind a few nuances.The length of the interval can not be precisely calculated..The scale and units can not match

But how to find the length of the segment with the highest or absolute certainty?For each dimension of the space has its own formula.Consider a simple, one-dimensional case.Cartesian system of one-dimensional case is an ordinary coordinate line.In real

life, we are faced with hundreds of examples of the different coordinate lines.This line and the construction of the roulette, and the tailor's tape, and even track where each kilometer is marked by the number.There is nothing easier than to measure the length of the one-dimensional space.Particularly easy, if the beginning of the segment coincides with the reference (zero) coordinate axis.In this case, its length will match the coordinates of its end module.For example: if the segment emerges from the ground, and it has an end coordinate 5, the length of the segment will be equal to five.also no problem easier than how to compare two segments emanating from the ground.More will be the length of whose coordinates module will be great.For example: from the ground on the coordinate plane in different directions out two lengths.The coordinate of the segment, leaving the left is equal to -7, and coming to the right - 4. The module is the first segment 7 with a "+", and the second module - 4 with the same sign.Hence the first segment is longer than the second.If the segment does not start at zero, then you should use a universal formula for calculating the length of the one-dimensional space.It goes as follows: "In order to find the length of the segment in one-dimensional space is necessary because of the coordinate value of the right to deduct the value of the end of the coordinates of the left end."

task is similar to how to find the coordinates of the midpoint, but in this case, the coordinates are subtracted rather than added and divided by two.Consider an example.Let the segment has a beginning at 2 and ends at 11. Find the length of the segment.To subtract this value from the left-right coordinates: 11-2 = 9. A. 9. It should be noted that it is possible on the contrary, to subtract from the right end coordinate of the left, but then have to take the result in its absolute value (modulus).2-11 = -9.The module is -9 9. The result did not change.This technique can help solve specific tasks.You should also consider the examples of two-dimensional space.

For the two-dimensional space, there are special formulas that are a generalization of the one-dimensional case.Now consider a specific example for explaining the path of formula solutions.To address it is necessary to know the name of the segment connecting the two points of the circle.This segment is called a chord.Dan A chord with ends (1; 1) and B (4, 5).Find the length of segment AB.The length of the segment AB is equal to the square root of the arithmetic sum of the squares of the differences between corresponding coordinates of the points.This form is derived from the Pythagorean theorem.Now, in order.To find the difference between the respective coordinates must be the x-coordinate of a point deducted in the x-coordinate of point A. We get 4-1 = 3. We carry out the same operation for the y-coordinate.We get 5-1 = 4. Now each obtained difference squaring: 3 * 3 = 9.4 * 4 = 16.The results add up: 9 + 16 = 25.Next, take the square root.The root of 25 = 5. Answer: The length AB = 5.