Geometry Coordinate Proofs

Introduction of  Geometry Coordinate:

             A coordinate is a number that determines the location of a point along some line or curve. A list of two, three, or more coordinates can be used to determine the location of a point on a surface, volume, or higher-dimensional domain.

            For example, the longitude is a coordinate, which determines the position of a point along the Earth's equator, and latitude is another coordinate that defines a position along a meridian. The pair of coordinates consisting of latitude and a longitude determines a point on the surface of the Earth.

Geometry Coordinate Proofs Example:

In geometry, prove that the segment created by joining the midpoints of two sides of a triangle is parallel to the third side and has a distance end to end equal to half that of the third side.

                     

Solution:

            There may be a definite amount of doubt that the shape above is completely common. If we show that theorem for the above figure, have we actually proven it for all similar triangles? It would appear that this is a particular triangle, indeed, that has one side on the x-axis and one vertex at the origin in geometry

            The common formula for distance between two spots will allow us to determine the required length. The formula tells us that for any two spots (x₁,y₁) and (x₂,y₂) the length of the circle of segment between then.

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Trigonometry Radian Measure

Introduction:

       An angle is determined by rotating a ray about its endpoint. One way to measure angles is in radians. To signify that a given angle is in radians, a superscript c, or the abbreviation rad might be used. If no unit is given on an angle measure, the angle is assumed to be in radians. `(3pi^c)/2-=(3pi)/2 rad.-=(3pi)/2`                                                                                                                       

Trigonometry Radian Measure:

        Middle angles of a circle contain an angle measure of 1° if it subtends an arc to be 1/360 of the boundary of the circle. These appearances of angle determine is reasonably general. Another appearance of angle determine namely in utilize is radian measure. If a middle angle subtends an arc i.e. identical toward the radius of the circle after that the middle angle contain a computing of one radian.

If a middle angle θ of a circle through radius r subtends an arc of length s, subsequently their radians establish is describing since  `theta= s/r`

Given, radius is 4 cm, and length of arc is 60 cm.

We know that the formula for radian measure of `theta=s/r` .

As a result,`theta = 60/4`

θ=15

The angle of the arc is 15 radians.

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Explain Rotational Symmetry

Introduction:

           The rotational symmetry is objects that look the same after a certain amount of rotation. A object may have more than 1 rotational symmetry for instance, if reflections or turning it over are not counted, the trickling appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry").

Key Factors of Rotational Symmetry:-

• The rotational symmetry is proportion with value to some or all rotations in m-dimensional Euclidean space.

• Rotations are through isometrics, i.e, isometrics preserve orientation.

• herefore a proportion group of revolving symmetry is a subgroup of E+ (m)

• Rotational symmetry by way of admiration to all rotations about all points implies translational regularity with respect to all translations, so space is all the same, and the rotational symmetry group is the whole E (m).

• The rotational symmetry through deference to any angle is, in two extents, circular symmetry. The basic domain is a half-line.

• That is, no dependence on the angle use cylindrical coordinate and no dependence on either angle using spherical coordinates.

• The basic sphere of influence is a half-plane from side to side the axis, and a radial half-line, correspondingly.

• Ax symmetric or ax regular are adjectives which refer to an object have cylindrical symmetry, or ax rotational symmetry.

• In mains, continue or separate rotational regularity about a plane correspond to correspond mains rotational symmetry in every perpendicular plane, about the point of intersection.

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Common Data Representation

Introduction to Common Data Representation:

Representing a Numerical Data:
             A numerical data is a set of mathematical values which is used for measuring and counting and it can be represented by graphs(Pie-chart, bar graph). A numerical value is generally used for scaling purposes i.e. to find out the range, value ,mean and count of a particular object. We can even represent the data on number line based on the values. Depending on values we can represent data in statistical tables and can give ranks to the data, we can even find frequency distribution.
We can represent the Data by:
Pie Chart:

     Pie chart is a representation on a circle. Therefore its also known as "circle graph". The circle is divided into different partition depending on Category. It is one of the most common graphs for describing a set of measurements. It is the best graphical display for displaying data arranged in categories. Each category is represented by a wedge of the pie and the size of each wedge is in proportion to the percentage of each category.

Bar Graph:

     A bar graph consist two axes and a series of horizontal bars or vertical bars which are placed in the x ,y plane,depending on the value. It is another way of displaying qualitative data.The frequencies along the vertical axis (ordinate) of the chart and the categories on the horizontal axis of the chart(abscissa). Bar chart is used to display frequency and percentages.
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How to multiply decimals

Introduction to Multiplying decimals:

         A number that contains the decimal point is called as decimal. The decimal numbers are always has ten as its base value. In Hindu-Arabic numeric system, decimal notation refers the positional notation of the number. It can also used to refer the non-positional system in Roman and Chinese numerals. Decimals are always can be represented as another form of fractions.

Place Value:

       To know the decimals, we need to understand the place value. The value of a digit can be determined by its position in a number is called as place value. Each place in a decimal number has a different place value.

For Example, 25.64

Here 2-tens

         5-ones

         6-tenths

         4-Hundredths      

Multiplying Decimals:

Rules for multiplying Decimals:

• Multiply the numbers normally, ignoring the decimal points.

•  After multiplying normally, put the decimal point in the answer – The answer will have as many decimal places as the two given numbers combined.

 Consider the following Example,

              13.7* 12.5

Step1: Multiply normally by ignoring the decimal points

              137*

              125

             685

           274

         137 

        17125

How to find the Mean and Median of a data set

INTRODUCTION:

           A group of variables or a set of information is referred as Data. In general, sets are the collections of numbers and set can contains any kind of data. Data set is nothing but a collection of data. Data set can be represented as tables and graphs. Data collection is the method of collecting or preparing the data. For a given data set, we can find the mean, median, mode and range which is explained below.

Mean of data set:
         For finding the mean of all the values in a given data set, we have to find the sum of all numbers given in data set and we have to divide the total sum by the total number of elements.
Example:
Find the mean of data set: {8, 18, 23, 35, 51}
Solution:
         Mean      =    Total sum of data set  / Total number of elements in data set
                         =    (8 + 18 + 23 +  35 + 51) / 5
                         = 135 / 5   = 27
Median of a data set:
        In general, median is referred as the middle value of the given data set.
Example 1 :
Find the median for the given values: {5, 6, 9, 25, 34}
Solution:
      Here, the middle value is 9. Hence median = 9. 

How to translate word problems into algebraic expression

Introduction:

             Translating words into algebraic expression is the process of translating the word problems into an algebraic expression which can be used to solve the word problem and produce the solution for the given words problem. It is the simple way to solve words problem. Let us discuss about translating the words into algebraic expression.

Example problems to translating words into algebraic expression:

Problem 1:
Flowers shop has thirty Roses and forty Lilly. How many pieces of flowers does flowers shop have? 
Solution:
            Let a = Total number of Flowers in the flowers shop.
            The sum of thirty Roses and forty Lilly is equal to the total number of flowers in the flowers shop. It translates the words problem into an algebraic expression.
            a = 30 + 40
Solve this expression.
            Let a = Total number Pieces of Flowers in the flowers shop
                  a = 70.
There are 70 Pieces of Flowers in the flowers shop.

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