Introduction :

Standard reference point which shows the particular place in a segment for representation.The centre of the axes will be the origin.We can write the xy coordinates with the points coordinates, In
this article we have the formulas for xy coordinates and the problems xy coordinates points.In the standard reference point two axes represents the line segment such as parallel lines and the
points.

Standard Reference Point:

Standard reference point we have the following parameters such as distance between the two points,midpoint of the line segment and the slope of the line.In two dimensional space system we have
the two axes coordinates only namely (x,y).

Distance between two points:

By using the coordinate plane we can measure the distance between the two points given such as (x1,y1) and (x2^,y^2).

d = `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

Midpoint:

Mid point is described as a halfway point where the line segment divided into two equal parts.

m = ` ((x_1+x_2)/(2))`,`((y_1+ y_2)/(2))`

Slope of a line:

Slope of line 'm' can be find by the formula with the coordinates points given such as (x1,y1) and (x2,y2).

m =` (y_2-y_1)/(x_2-x_1)`

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Problems with Standard Reference Point:

Example 1:

Find the distance coordinates between the points given are A(2,3) and B (6,0).

Solution:

Let "d" be the distance between A and B. (x1,y1)= (2,3), (x2,y2)= (6,0)

Then d (A, B) = `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

= `sqrt((6-2)^2 +(0-3)^2)`

= `sqrt((4)^2+(-3)^2)`

= `sqrt(16+9)`

=`sqrt 25`

= 5

Example 2:

Find the mid point coordinates of line segment joining given points A(6,4) and B(2,0)

Solution:

The required mid point is

Formula = ` ((x_1+x_2)/(2))`,`((y_1+ y_2)/(2))` here, (x1, y1) = (6,4),(x2, y2) = (2,0)

= `((6+2)/(2))``((4+0)/(2)) `

= ` (8/2)`` (4/2)`

= (4,2)

Example 3:

Find the slope of the line whose point coordinates are (3,4) and (4,2)

Solution:

(x1 y1) = (3,4), (x2 y2) = (4,2),

Formula for slope of a line m =` (y_2-y_1)/(x_2-x_1)`

m = ` (2-4)/(4-3)`

= `(-2/1)`

m = -2