# Co-ordinate Geometry Formulas

**Co-ordinate Geometry Formulas**

co-ordinate geometry is one of the most important part of mathematics.

In **co-ordinate geometry** we study about the geometry of different objects which are represented as shape made by points in a co-ordinate plane or graph.

Use of co-ordinates in geometry makes geometry more easier to calculate. Some of the important formulas used to formulate equations in co-ordinate geometry are;

Quadrants and sign of co-ordinates:

1. In first quadrant, (+, +)

2. In second quadrant, (-, +)

3. In third quadrant, (-, -)

4. In forth quadrant, (+, -)

Where first sign is for x-co-ordinate and second sign for y-co-ordinate

5. Distance between the line Ax + By + c = 0 and the given ordinate

is:

6. When equation Ax + By + C = 0 is reduced in the form of then the required equation is:

7. The distance between any two points and is given by

8. The distance between any two points and origin (0, 0) is given by

9. The co-ordinate of the point which divides a straight line joining the given points internally in the ratio is given by

Or,

is section formula.

10. The co-ordinate of the point which bisects the line joining two given points and is given by

and,

If the point divides AB in the ratio k:1 then

and,

11. The co-ordinate of the centroid of a triangle ABC whose vertices are and is the given by

and

12. a. the area ABC whose vertices are

and is given by

=

b. if one of the vertices of is the origin

13. let and be the vertices of a quadrilateral. Then the area of quadrilateral ABCD is

**EQUATION OF STRAIGHT LINES**

1. the slope of the line joining two points and is given by,

a. slope of the line

b. when the equation of line is given, (ax + by – c = 0) then slope of line =

2. equation of straight line in slope & intercept form is y = mx + c where m is slope and c is x-intercept

3. when the line passes through the origin, then c = 0 & equation is y = mx.

4. When the line is parallel to x-axis, then the equation is y = h.

5. When the line is parallel to y-axis then the equation is x = a.

6. Equation of straight line in double intercept form is,

7. Equation of straight line in normal (perpendicular form is, .

8. Equation of a line passing from two points and is

9. Equation of line passing from a point & slope ‘m’ is,

10. The angle between two lines and is where = slope of first line & = slope of second line.

11. When two lines are parallel, then (their slope is equal)

12. When tow lines are perpendicular, then .

13. The angle between two lines is,

**PAIR OF LINES**

1. The general equation of any line through the intersection of two lines and is where k is given by and is the point of intersection of the two lines.

2. If represents the equation of a pair of straight lines through the origin, then are the equation of two straight lines represented by the homogeneous equation of the second degree.

3. The angle between a pair of lines represented by the equation is given by, if i.e. the straight lines are coincident. If i.e. the straight lines are perpendicular.

4. The equation of a circle of radius (r), centre at origin is

5. The equation of a circle of radius (r), center at (h, k) is

6. Let AB be the diameter of a circle & the co-ordinates of A and B be . Then the diameter form of equation of a circle is .

7. Equation of tangent to the circle at is

8. Equation of tangent to the circle at is

The second degree general equation which may represent pair of straight lines

=

=

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