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ANALYTIC GEOMETRY - Coggle Diagram
ANALYTIC GEOMETRY
Slope (Gradient) Of A Straight Line The Slope of a straight line shows how steep a straight line is: Divide the change in height by the change in horizontal distance . Slope can be found by using the tangent of the angle of inclination.
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Vertical Lines are the lines which are parallel to y-axis m = tan90 = ∞ so that vertical lines have no slope or we can say
the slope of vertical lines are undefined.
Horizontal Lines are the lines which are parallel to x-axis. m =tan0 = 0 so that horizontal lines have a slope of 0.
Collinear points have same slopes If the points A, B and C are collinear points,
then mAB = mAC = mBC
Parallel and Perpendicular Lines d1 and d2 are two lines, m1 and m2 are the slopes of the lines. md = tanθ
mℓ = tanθ So; m1 = m2 then d1 // d2
and If d ⊥ ℓ md = tanα =
mℓ = tanθ = -tanβ = So; m1. m2 = -1 then d1 ⊥ d2
Equation of the lines which are passing through the origin can be found by y = mx (m is gradient of line) formula.
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Let A, B, C, D are the vertices of a parallelogram ABCD and K be the intersection of diagonals. Since K is the mid-point of the diagonals x1 + x3 = x2 + x4 and y1 + y3 = y2 + y4
Equation of a line parallel to x-axis md=0 0= y-b/x-a , y-b =0 y=b
Equation of a line parallel to y-axis md is not defined since tan90 is not defined so x-a 0 since md =y-b/x-a is not defined x=a
Straight Line Graphs To be able to draw a straight line, we need to know at least two different points that the line passes throughAfter the points are plotted on Cartesian coordinate plane, draw a straight line passing on the points.
If the equation of the line is given ax + by = 0 form or y = mx form, the graph of line passes
on origin.
If the equation of the line is given by + c = 0 form or y = b form, the graph of line is parallel
to x-axis.
If the equation of the line is given ax + c = 0 form or x = a form, the graph of line is parallel
to y-axis.
The distance between two points A(x) and B(y) on the number line is the absolute value of the coordinates of these points.
| AB | = | x-y | = | y - x |
The horizontal axis (x-axis) and the vertical axis (the y-axis)intersect at the origin O and naturally divide the
Cartesian plane into 4 quadrants labeled quadrants I, II, III and IV.
We use the notation ( x , y ) to represent an ordered pair, notice that the x-coordinate or abscissa is first, followed by the y-coordinate or ordinate listed second.
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Slope of a Line Passing Through Two Points A(x1,y1) and B (x2,y2) is m = y2-y1/x2-x1
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Equation of a Line in Slope – Point Form Let A (x1 ,y1 ) is a point on the line ℓ and slope of the line is m, the equation is, y-y1 = m ( x - x1 )
Equation of a Line in Two Point Form A(x1,y1) and B (x2,y2) on the line is y-y1/x-x1 = y2-y1/x2-x1
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Standard equation of a line ax + by + c = 0 is the standard equation of a line (a, b, and c are constants). This form is usually
gotten by manipulating the slope intercept form or the two intercept form.
Equation of a line passing through origin the line d passing through the point (0,0) has slope m = y-0/x-0 so y=mx
Finding the Slope of the Line with a Given Equation ax + by + c = 0 is linear equation of a line, y = mx + n is functional form of a line . The slope of a line given in the form y = mx + n is m.
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