## ANALYTICAL GEOMETRY FORMULAS

 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 Bd = √(x₂ - x₁) ² + (y₂ - y₁) ² Area of triangle using three vertices Area of triangle if three vertices of triangle are given. 1⁄2 {x1(y2-y3) + x2(y3-y1) + x3(y1-y2)} Area of quadrilateral Area of the quadrilateral if four vertices of quadrilateral are given. 1⁄2{(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)} 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 of the line segment 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 θm = (y2 - y1)/(x2 - x1)m = - coefficient of x /coefficient of yy = m x + bm-slope Equation of the line 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 + bHere 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 Perpendicular distance a point and a line The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is     d =   | (ax₁ + by₁ + c)/ va² + b² | 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 | Angle between two lines θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)| Equation of circle (x-h)² + (y-k)² = r² Equation of circle with two endpoints of diameter (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) Condition of two circles touching externally c₁c₂ = r₁ + r₂ Condition of two circles touching internally C₁ C₂ = r₁ - r₂ 2 g₁g₂+2f₁f₂=c₁+c₂ • Area of triangle worksheets
• Centroid of the triangle worksheets
• 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) Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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