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ANALYTIC GEOMETRY - Coggle Diagram
ANALYTIC GEOMETRY
ANALYTIC OF LINES
SLOPE
Slope (denoted by the letter m) is numerical measure of a line's inclination relative to the horizontal.
Slope is calculated by finding the ratio of the vertical change to the horizontal change between (any) two distinct points on a line. Slope also can be found by using the tangent of the angle of inclination.
For acute angles tanθ value will be positive, for obtuse angles tanθ value will be negative.
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LINE EQUATIONS
Equation of a Line in Slope - Point Form: y - y₁ = m.(x - x₁). Also equation of a line that is passing through the origin can be found by using the y = mx, coefficient (m) of the x is the slope.
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Equation of a Line Parallel to X-Axis: Let P(a,b) is a point that is parallel to x-axis, we can denote the equation by y = b. Equation of a Line Parallel to Y-Axis: Let P(a,b) is a point that is parallel to y-axis, we can denote the equation by x = a.
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Finding the Slope of the Line with a Given Equation: We have to use the y=mx+b form to find the slope. You can easily see the slope since it is the coefficient of the x variable, or the number in front of x.
LINES
VERTICAL
Because the m = tan90° is undefined, the slope of vertical lines are also undefined.
HORIZONAL
m = tan0° is equal to 0, so that horizontal lines have a slope of 0 as well.
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STRAIGHT LINE GRAPHS
For straight line graphs there is a linear relationship between the x and y values. We should know at least 2 different points that the line passes through to draw a straight line.
If the equation is in the y = b form, the line is parallel to x-axis. If the equation is in the x = a form, then the line is parallel to y-axis. Also the form ax + by = 0 gives us the graph of line passes on origin.
ANALYTIC OF POINTS
THE CARTESIAN SYSTEM
We use the notation (𝑥,𝑦) to represent the ordered pair of points.
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If the point lies on abscissa, point y will be zero. If the point lies on ordinate, point x will be zero.
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FINDING THE MIDPOINT
Measure the distance between the two end points, and divide the result by 2.
The Mid-Point of the Diagonals of a Parallelogram: x₁ + x₃ = x₂ + x₄, y₁ + y₃ = y₂ + y₄
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