Cooridante Axes and Representation of a Point
The figure given alongwith is called the XY Cartesian plane. The line XOXâ€² is called the Xaxis and YOYâ€² the Yaxis.If P(x, y) is a point in this plane, then x is the Xcoordinate of P or abscissa of P and y is called the Ycoordinate of P or the ordinate of P.
Remember that Xcoordinate of the point is the distance of the point from Yaxis and Ycoordinate of the point is the distance of the point from Xaxis.
The XY Cartesian plane is divided into four equal parts called quadrants (I, II, III, IV).
Sign convention

1st 
2nd 
3rd 
4th 
Xaxis 
+ve 
ve 
ve 
+ve 
Yaxis 
+ve 
+ve 
ve 
ve 
Equation and Graph of Coordinate Axis
 Equation of X and Yaxis are Y = 0 and x = 0 respectively
 Equation of a line parallel to Xaxis is Y = b (b is constant)
 Equation of a line parallel to Yaxis is X = a (a is constant)
 Any point on the Xaxis can be taken as (a, 0) and any point on the Yaxis can be taken as (0, b).
 To find out X and Y intercepts of a line, we will put Y = 0 and X = 0 respectively in the equation of the line.
If you know the coordinates of two points:
 Find out the distance between them.
 â€‹Find the midpoint, slope and equation of the line segment formed by these two points.
Distance between two points
If there are two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) on the XY plane, then the distance between them is given byExample1
What is the distance between the points (3, 2) and (6, 6)?
Solution
Distance = = = 5 units.
Example2
Coordinates A and C of a square ABCD (points in order) are (4, 2) and (1, 4). What is the area of the square?
Solution
For square ABCD, line segment AC will be its diagonal.
AC = = units
Diagonal of square = = units
So, side of square = units
Hence, area = (Side of square)^{2} = = 6.5 sq. units
Methods to identify if three points A, B and C are in the same straight line:
If there are three points A, B and C, they may be in the same straight line or form a triangle.
Method 1:
Area formed by the three points = 0 [Formula to find out the area of triangle given ahead]
Method 2:
Slope of any two line segment AB or BC or AC are equal. For example, slope of line AB = Slope of line AC
Method 3:
Sum of any two line segment is equal to the equal to third line segment. For example, AB + BC = AC
Division of a line segment [if three points A, B and C are in a straight line]
 Internal
 External
The image of a point along the mirror place on a straight line
The image of A(x_{1},_{ }y_{1}) with respect to the line mirror ax + by + c = 0 be B(x_{2}, y_{2}) is given by
â€‹
â€‹
Foot of the perpendicular
If the foot of the perpendicular from (x_{1}, y_{1}) to the line lx + my + n = 0 is (h, k) then