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
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
is section formula.
10. The co-ordinate of the point which bisects the line joining two given points and is given by
If the point divides AB in the ratio k:1 then
11. The co-ordinate of the centroid of a triangle ABC whose vertices are and is the given by
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
- Distance Formula Basic Distance Formula. Distance formula to calculate distance between two...
- Vector Formulas Vector Formulas A vector can also be defined as an...
- Vector Geometry Formulas Vector Geometry Formulas Vector Geometry in simple words means...
- Trigonometric Addition and Subtraction formulae Trigonometric Addition and Subtraction formulae. Angle addition Addition and subtraction...
- Ratio and Proportion Formulas As you know Ratio is a relation between two quantities...