Trisecting a Line Segment

Introduction for line segment:

A line segment is the basic and fundamental topic in geometry and math subject. Generally in math, a straight and long line is divided with two definite end points on both sides are known as line segments. Here in this article we have to brief explain about line segment and trisecting a line segment. And use dome example figures for how to do trisecting line segment.

Line Segment General Definition:

In math, a line segment is can be defined as one small part or distance between the two endpoints of a long line.
Line segment is also shape like as ‘a straight line’, which is joining the two points with coordinates, and the line is infinity after that, the end points.
Example figure for general line segment:



In this figure xy is the infinity line, and A, B are the two end points, and the line segments are` bar (AB)` .
The length of the line segments AB would be written as `bar (AB)` . And the line segments have used the name as to be two end points AB.

Trisecting a Line Segment:

Trisecting a line segment is the one of the process of dividing the line segments with a new line and makes the new line segments.  It is simply defined as which is one line segment, is trisected.

First we have to draw a line segment, and then bisect the line segment with a new line, and then we have to get trisecting line segment.

Generally trisecting a line segment, we use compass and ruler and makes easy.

Step by step process for trisecting line segment:

Step 1:

First we have to draw a line segment with two end points A, B. And name of the line segment is AB.

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Then next, draw a new dotted line through endpoint A, but not coincident with AB, draw that line for our convenient and put an end point with the name of  C and D.

Step 3:

Here the line segment distances of AC and AD are equal.

Step 4:

Then again draw a dotted line through End point B, same length and put end points and named as E and F.

This E and F are opposite lines for AB from points C and D. distance BE = EF.

Step 5:

Connect CF and DE; those two lines will cut AB into third lines equal.

Example figure for trisecting line segment:



The above example figure and explanations will make clears for the trisecting a line segment.

Solving Centroid Formula

Introduction to solve centroid formula:

In general, Centroid formula is a point on a given body or shape at which the entire mass of the body acts (center of gravity of the mass), it might also be the center of area for certain shapes. For a triangle, solving centroid is the point at which the medians of the triangle intersect; they intersect at the ratio 2:1. In the case of polygons the Centroid is found using the boundary co-ordinates solving.

Solving Centroid Formulae:

In this case the Centroid of the triangle is taken and the formula used to find out solving the centroid of a triangle is,

G (x1+x2+x3)/3 , (y1+y2+y3)/3
Where,
(x1, y1)
(x2, y2)
(x3, y3)
are the co-ordinates of the triangle.

In general, for any shape in the x-y plane the Centroid formulae can be generalized to,
G (x1+x2+x3+….+xn)/3n , (y1+y2+y3+….+yn))/n
Where,
(x1, y1)
(x2, y2)
(x3, y3)
(........)
(........)
(xn, yn) are the co-ordinates of the given shape.

Example Problems on Solving Centroid Formula:

1. Calculate the Centroid of a triangle whose co-ordinates are (3, 6) (4, 2) (3, -4)

Sol:
The given points are (3, 6) (4, 2) (3, -4),
Therefore solving,
(x1, y1) is (3, 6)
(x2, y2) is (4, 2)
(x3, y3) is (3, -4)

Formulae for the Centroid of triangle is,
G (x1+x2+x3)/3 , (y1+y2+y3)/3
(3+4+3)/3 , (6+2-4)/3
(10)/3 , (8-4)/3
10/3 , 4/3
3.33 , 1.33
Therefore the Centroid is (3.33, 1.33)

2. Calculate the Centroid of a triangle whose co-ordinates are (4, 8) (3, 2) (5, -4)
Sol:
The given points are (4, 8) (3, 2) (5, -4),
Therefore solving,
(x1, y1) is (4, 8)
(x2, y2) is (3, 2)
(x3, y3) is (5, -4)

Formulae for the Centroid of triangle is,
G (x1+x2+x3)/3 , (y1+y2+y3)/3
(4+3+5)/3 , (8+2-4)/3
(12)/3 , (10-4)/3
12/3 , 6/3
4 , 2
Therefore the Centroid is (4, 2).

3. Calculate the Centroid of the quadrilateral, whose co- ordinates are (3, 2) (5, -4) (4, 2) (3, -4)

Sol:
The given points are (3, 2) (5, -4) (4, 2) (3, -4),
Therefore,
(x1, y1) is (3, 2)
(x2, y2) is (5, -4)
(x3, y3) is (4, 2)
(x4, y4) is (3, -4)

Formulae for the Centroid is
G (x1+x2+x3+….+xn)/3n , (y1+y2+y3+….+yn))/n,
(3+5+4+3)/4 , (2-4+2-4)/4,
(15)/4 , (4-8)/4,
3.75 , -4/4
3.75 , -1
Therefore the Centroid is (3.75, -1)

Three Horizontal Lines

Introduction to three horizontal lines:

Three horizontal lines are nothing but three lines parallel to x – axis or three lines perpendicular to y – axis. Three horizontal lines mean their slopes will be zero. Because the slope of x – axis is 0. We know if there is any two lines are parallel their slope s will be equal. We will some example problems for graphing three horizontal lines. If the line is horizontal their y value is constant.

Examples for three Horizontal Lines:
If the line is parallel to x – axis we can say those lines are horizontal lines. The slopes of the horizontal lines are zero and the y value of the line is constant. So the equation of the horizontal lines are like y = some constant value.Having problem with geometric probability formula keep reading my upcoming posts, i will try to help you.

Example 1 for three horizontal lines:

Graph the following lines y = 1, y = 5 and y = -1.

Solution:

Here the line equations are y = 1, y = 5 and y = -1

The slope intercept form general equation is y = mx + c

If we compare the given equation with general form we can get the slope of the lines are 0.

If we graph these equations we will get the graph like the following.



More Examples for three Horizontal Lines:
Example 2 for three horizontal lines:

Graph the following lines y = 2, y = 3 and y = -2.

Solution:

Here the line equations are y = 0, y = 3 and y = -2

The slope intercept form general equation is y = mx + c

If we compare the given equation with general form we can get the slope of the lines are 0.

If we graph these equations we will get the graph like the following.



In this the line y = 0 is lies on the x axis.

These are some of the examples for three horizontal lines. From the above we can understand how to graph the three horizontal lines and slopes of the horizontal lines.