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 using three vertices |
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})} | |
Centroid of the triangle | |
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 | |
Slope of the line |
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 | |
General equation of circle |
x² + y² + 2gx + 2fy + c = 0 |
Length of the tangent |
√ (x₁² + y₁² + 2gx₁ +2fy₁+c) |
c₁c₂ = r₁ + r₂ | |
C₁ C₂ = r₁ - r₂ | |
2 g₁g₂+2f₁f₂=c₁+c₂ |
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