ANALYTICAL GEOMETRY FORMULAS
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Name of the topic |
Formula |
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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  |
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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 |
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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)} |
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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)} |
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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 |
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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 |
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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 |
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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. | |
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Slope intercept form: y = m x + b Here m = slope and b = y-intercept | |
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Two point form: (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁) | |
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Point- Slope form: (y-y1) = m (x-x1) | |
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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 |
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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)| |
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(x-h)² + (y-k)² = r² | |
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(x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0 | |
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General equation of circle |
x² + y² + 2gx + 2fy + c = 0 |
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Length of the tangent |
√ (x₁² + y₁² + 2gx₁ +2fy₁+c) |
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c₁c₂ = r₁ + r₂ | |
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C₁ C₂ = r₁ - r₂ | |
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2 g₁g₂+2f₁f₂=c₁+c₂ |
- Area of triangle worksheets
- Section formula worksheet
- Centroid of the triangle worksheets
- Triangle with three vertices
- Finding missing vertex using centroid worksheet
- Distance between two points worksheet
- Equation of line using two points worksheet
- Equation of the line using point and slope worksheets
- Point of intersection Worksheets
- Concurrency of straight lines worksheet
- Circumcentre of Triangle Worksheet
- Orthocentre of Triangle Worksheet
- Equation of the line worksheet
- Equation of the line worksheet(mixed formulas)
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WORD PROBLEMS
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Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
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OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
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
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