Coordinate Geometry

Coordinate Geometry

Cartesian Coordinates

For locating the position of a point on a plane, we require a pair of the coordinate axis.

X and Y-Axis

The left-right (horizontal) direction is commonly called X or The distance of a point from the y-axis is called its x-coordinate, or abscissa.

The up-down (vertical) direction is commonly called Y or The distance of a point from the x-axis is called its y-coordinate, or ordinate.

The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y).

The point where x-axis and y-axis intersect is called the origin. Its coordinates are (0,0).

 

The ordinates of all points on a horizontal line which is parallel to the x-axis are equal i.e. y = constant = 2.

The abscissa of all points on a vertical line which is a line parallel to the y-axis is equal i.e. x = constant = 4.

 

Four Quadrants of Coordinate Plane

The rectangular axes X'OX and Y'OY divide the plane into four quadrants as below :

 

The coordinates of the points in the four quadrants will have sign according to the below table:

Quadrant

x-coordinate

(abscissa)

y-coordinate

(ordinate)

Ist Quadrant

+

+

IInd quadrant

-

+

IIIrd quadrant

-

-

IVth quadrant

+

-

 

 

DISTANCE FORMULA

The distance between two points (x1, y1) and (x2, y2) in a rectangular coordinate system is equal to

 

The distance of a point (x, y) from the origin is 

 

SECTION FORMULA

 

A point P(x,y) which divide the line segment AB in the ratio m1 and m1 is given by

The midpoint P is given by

Remark: To remember the section formula, the diagram given below is helpful:

 

Area of Triangle ABC

Area of triangle ABC of coordinates A(x1,y1) , B(x2,y2) and C(x3,y3) is given by

For point A,B and C to be collinear, The value of A should be zero, i.e. A=0.

How to solve general Problems of Area in Coordinate geometry-

Area of Triangle

Three vertices will be given, you can calculate the area directly using formula

Area of Square

Two vertices will be given, we can calculate either side or diagonal depending on vertices given and apply the square area formula

Area Of rhombus

Given: all the vertices coordinates

Two ways

1) Divide the rhombus into two triangle. Calculate the area of both the triangle and sum it

2) Calculate the diagonal and apply the Area formula

Area of parallelogram

Three vertices are sufficient to find the area of a parallelogram

Calculate the area of the triangle formed by the three vertices and double it to calculate the area of a parallelogram

Area of quadrilateral

Given: all the vertices coordinates

Divide into two triangles. Calculate the area separately and sum it

For detailed Class 10 Mathematics Notes, visit- edusaksham.com

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