POINTS IN GEOMETRY

POINTS

Point is represented by dot. A point has position but not size.

Example:

A point on the line.

A point in the space.

here point P,Q and R are on the line

and

Point X,Y and Z in the space.

In two dimensional point can be any of the four quadrant. 

i.e.

1. First quadrant: In which both x and y co-ordinate are positive. It is represented by (+x,+y)
2. Second quadrant:In which x is negative and y co-ordinate is positive. It is represented by (-x,+y)
3. Third quadrant: In which both x and y co-ordinate are nagetive. It is represented by       (-x,-y)
4. Fourth quadrant:In which x is positive and y co-ordinate is nagetive. It is represented by (+x,-y)

DISTANCE BETWEEN TWO POINTS:

If the two points A and B of coordinate (x1,y1) and (x2,y2) are given then the distance between AB is given by the following formula.

For example:

Let the two points are (3,2) and (7,8)

Distance formula=

AB=√(7-3)²+(8-2)²

AB=√4²+6²

AB=√16+36

AB=√52

Mid point formula

If the two points A and B of coordinate (x1,y1) and (x2,y2) are given then the mid point of AB is given by the following formula.

Find the value of K if the points A(3k, k) and B(3k+1, k-3) are equidistant from the origin.

Distance formula= √(x-x1)²+(y-y1)²

where (x,y) are given point and (x1,y1) are origin.

then 

√((3k)²+k²)=√((3k+1)²+(k-3)²

sovle for k

(3k)²+k²)=(3k+1)²+(k-3)²

9k²+k²=9k²+1+6k+k²+9-6k

simplfy

0=10

conclusion: for all value of k, points A(3k, k) and B(3k+1, k-3) are equidistant from the origin.

Work for you:

1. Find the quadrant in which following points lie:

• (5,2)
• (-2,-2)
• (3,-3)
•  (-2,1)

2. Find the distance between following points

• (5,2) and (2,5)
• (-3,-3) and (-2,-2)
• (1,2) and (-2,1)

3. Find the mid point of points

• (5,-2) and (-2,5)
• (3,3) and (-2,-2)
• (2,-1) and (-2,1)