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ANALYTIC GEOMETRY - Coggle Diagram
ANALYTIC GEOMETRY
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THE COORDINATE PLANE
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- Plotting Ordered Pairs In The Cartesian Plane
To plot the point (-2,3), go 2 units to the left of the origin on the x-axis then move 3 units up parallel to the y-axis. The point corresponding to the ordered pair (-2,3) is labeled in the figure below and is located in Quadrant 2.
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NOTE: -If abscissa of a point is zero, the point lies on y axis. If ordinate of a point is zero, the point lies on x axis.
- Finding The Distance Between Two Points Using The Distance Formula
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- Dividing Line Segment Into Proportional Parts
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- Finding The Midpoint Of A Line Segment Using The Midpoint Formula
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Let A, B, C, D are the vertices of a paralellogram ABCD and K be the intersection of diagonals. Since k is the mid- point of the diagonals .
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- Center Of Gravity Of A Triangle
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(x1+x2+x3)/3,(y1+y2+y3)/3
LINES IN PLANE
- Slope (Gradient) Of A Straight Line
The slope of a straight line shows how steep a straight line is. The method to calculate the slope is: Divide the change in height by the change in horizontal distance
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- Vertical lines are the lines which are parallel to y-axis
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- Horizontal lines are the lines which are parallel to x-axis
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- Slope Of A Line Passing Through Two Points
The slopenof a line passing through the points A(x1,y1) and B(x2,y2) is m=y2-y1/x2-x1
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EXAMPLE :check:
A(0,0) and B(1,7)= 7-0/1-0=7
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- Parallel And Perpendicular Lines
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- Collinear Points Have Same Slopes
If the A, B and C are collinear points then mAB= mAC=mBC
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LINE EQUATIONS
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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 Parallel To X-Axis
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- Equation Of A Line Parallel To Y-Axis
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- Equation Of A Line Passing Through Origin
The line passing through the point (0,0) has slope m= y-0/x-0
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- Relative Position Of Two Lines
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