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ANALTYIC GEOMETRY. - Coggle Diagram
ANALTYIC GEOMETRY.
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
Distance between two points
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 {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
(x₁ + x₂)/2 , (y₁ + y₂)/2
Midpoint is the point which is exactly in the middle of the line segment joining two points (x1,y1) and (x2,y2)
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
Equation of the line
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
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.
Perpendicular distance a point and a line
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 |
The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is
d = | (ax₁ + by₁ + c)/ va² + b² |
Angle between two lines
θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)|
