Learn Points and Lines

To learn about points and lines, A point used to represent a place in a plane with a help of pencil, a point is nothing but the dot , it has no dimension or no width, it’s only a simple black dot. In geometry co ordinates of a point which shows the particular place in a segment for representation.Line has two end points is called segment. Line segment is denoted with a connected piece of line.line segments names  has two endpoints and it is named by its endpoints.


learn about points and lines:

To learn about the geometric points and lines we have to know the classification of a points and lines.points and lines classification are as follows.
Collinear points:
When three or more points lies on the same line is said to be collinear points.

Midpoint:
A halfway point where line segment divides into two equal parts are called midpoint.

Equidistant point:
A point which is said to be equidistant in a line segment where point is equal length from other points which are in congruent then the point is equidistant point.

Parallel line segment:
Two lines which does not touch each other are called parallel lines.

Perpendicular line segment:
Two line segment  that form a L shape are called perpendicular lines.


learn problems in points and lines:

Example 1:
Find the distance between the points A(5,2) and B (7,3).


Solution:
Let assume "d" be the distance between A and B.           (x1,y1)= (5,2), (x2,y2)= (7,3).

Then d (A, B) =`sqrt((x2-x1)^2+(y2-y1)^2)`

= `sqrt((7-5)^2 +(3-2))^2)`

= `sqrt(2^2+1^2)`

= `sqrt(4+1)`

=`sqrt5`

Example 2:
Find co-ordinate of the mid point of the line segment joining given points A(-1,1) and B(3,4)

Solution:
The required mid point is
Formul a   `((x_1+x_2)/2 ,(y_1+y_2)/2)` here,  (x1, y1) = (-1,1),(x2, y2) = (3,4)

=  `((-1+3)/(2))``((1 +4)/(2)) `

= `(2/2) ` ,  ` (5/2)`

=`(1,5/2)`

Example 3:
Find the slope of the lines given (2,-1) and (1,3)

Solution:
(x1,y1)= (2,-1), (x2,y2)= (1,3).
We know to find slope of line,m=` (y_2-y_1) /(x_2-x_1)`

=`(3+1)/(1-2)`

m =`4/-1` = -4
Example 4:

Find the equation of the line having slope `1/2` and y-intercept −3.
Solution:
Applying the equation of the line is y = mx + c
Given,       m = `1/2` ,c = −3
y = `1/2` x + (−3)

or  2y = x − 6
or  x− 2y − 6 = 0.