In this page analytical geometry formulas we are going to see list of formulas which are used in the topic analytical geometry.
Name of the topic |
Formula |
Section formula (Internally) |
The formula to find the point which is dividing the line segment AB internally in the ratio m:n is given by |
Section formula (externally) |
The formula which is used to find the point which divides the line segment AB externally in the ratio m:n is given by |
To find the distance between two points A and B d = √(x₂ - x₁) ² + (y₂ - y₁) ² | |
Area of triangle if three vertices of triangle are given. ^{1}⁄_{2} {x_{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})} | |
Area of the quadrilateral if four vertices of quadrilateral are given. | |
^{1}⁄_{2}{(x_{1}y_{2}+x_{2}y_{3}+x_{3}y_{4}+x_{4}y_{1})- (x_{2}y_{1}+x_{3}y_{2}+x_{4}y_{3}+x_{1}y_{4})} | |
There are three medians of the triangle and they are concurrent at a point O,that point is called the centroid of a triangle. In the following diagram O is the centroid of ABC.Now let us look into the formula. = (x1+x2+x3)/3, (y1+y2+y3)/3 | |
Midpoint is the point which is exactly in the middle of the line segment joining two points (x1,y1) and (x2,y2) | |
(x₁ + x₂)/2 , (y₁ + y₂)/2 | |
The angle theta between the straight line and the positive direction of the X axis when measured in the anticlockwise direction is called angle of inclination.The tangent of the angle of inclination is called slope or gradient of the line. | |
m = tan θ m = (y2 - y1)/(x2 - x1) m = - coefficient of x /coefficient of y y = m x + b m-slope | |
A linear equation or an equation of the first degree in x and y represents a straight line.The equation of a straight line is satisfied by the co-ordinates of every point lying on the straight line and not by any other point outside the straight line. | |
Slope intercept form: y = m x + b Here m = slope and b = y-intercept | |
Two point form: (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁) | |
Point- Slope form: (y-y1) = m (x-x1) | |
Intercept form: (X/a) + (Y/b) = 1 | |
The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is | |
Distance between two parallel lines |
Distance between two parallel lines a x + b y + c₁ = 0 and a x + b y + c₂ = 0 d = | (c₁ - c₂)/ va² + b² | |
θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)| | |
(x-h)² + (y-k)² = r² | |
(x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0 | |
x² + y² + 2gx + 2fy + c = 0 | |
√ (x₁² + y₁² + 2gx₁ +2fy₁+c) | |
c₁c₂ = r₁ + r₂ | |
C₁ C₂ = r₁ - r₂ | |
2 g₁g₂+2f₁f₂=c₁+c₂ |
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WORD PROBLEMS
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OTHER TOPICS
Time, speed and distance shortcuts
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Domain and range of rational functions
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Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits