Does Geometry use Integers

The geometry generally use the integers and the variables. The answer for the question "Does geometry use integers?" is yes, the geometry uses the integers.For specific purpose of using the geometry with integers, the separate topic available as algebraic geometry. The integers are used for to represent the co-ordinates in vertex, some equations of the line in the 2d geometry. The examples and practice problems are given below for the question "Does geometry use integers or not?".

some examples to explain "does geometry use integers"

• Consider the given points  (4,4), (2,3), (8,3), (6, 2 ), (5, 1) and plot them in the graph. And also we have to denote the quadrant in which each of the point lies.

Solution:

The plotted points in the coordinate plane are shown in the graph. All the co-ordinates of the points are in positive so all will be in the first quadrant itself. And also that  the co-ordinates of the points are not having the zero term, they are all having only the non-zero values. Therefore the points are not lie on the x-axis and the y-axis.

• Consider the points (−3, −4) and (−9, 11) and find the horizontal and the vertical distances between them.

Solution:

For the points (−3, −4) and (−9, 11) The horizontal distance between the two points is a distance between the point corresponding to x coordinates−3 and −9 on the number line x- axis; i.e., (−3) − (−9) = 9 − 3 = 6. and the vertical distances between the two points is the distance between the points corresponding to y co-ordinates −4 and 11 on the number line y axis; i.e., (11) − (−4) = 15.

some more problems to explain "does geometry use integers"

• Consider the line passing through (5,6) and (15,9) and state whether the line is rising up or falling down find the slope.

Solution:

Take (5,6) as (x₁, y₁) and (15, 9) as (x₂, y₂). Then the slope of the line is

m = y₂-y₁ / x₂-x₁

  = `(9-6)/(15-5)`

  = `3/10`

The slope is a positive(+ve) number and so the line is rising up. Here the geometry is used to determine(find) the direction of the lines using the integers.

• Consider the line passing through (−16, 29) and (40, −6) and state whether the line is rising up or falling down and find the slope.
  

Solution:

The slope of the line is

m = y₂-y₁ / x₂-x₁

  = `(-6-29)/(40-(-16))`

  = `-35/56` 

  = `-5/8`

Here m is a negative number, the line will be falling down

In this problem the geometry is used to determine the direction of the lines using the integers.