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 ![]() |
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To find the distance between two points A and B d = √(x₂ - x₁) ² + (y₂ - y₁) ² |
Area of triangle using three vertices |
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Area of triangle if three vertices of triangle are given. 1⁄2 {x1(y2-y3) + x2(y3-y1) + x3(y1-y2)} |
Area of the quadrilateral if four vertices of quadrilateral are given. | |
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1⁄2{(x1y2+x2y3+x3y4+x4y1)- (x2y1+x3y2+x4y3+x1y4)} |
Centroid of the triangle | |
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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) | |
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(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. |
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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 | |
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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 | |
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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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