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I would like to coin together certain properties of [#permalink]
28 Dec 2006, 20:27

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I would like to coin together certain properties of Coordinate Geometry (from the basics) that I learnt from various sources, some even from the forum. Would appreciate your help in adding more or correcting these.

SLOPE:

slope m=(y1-y2)/(x1-x2)

*A straight line with a -ve slope passes through II and IV quadrants
A straight line with a +ve slope passes through I and III quadrants

*If the slope is 1 the angle formed by the line is 45 degrees

*If the slope of a line is n, the slope of a line perpendicular to it is its -ve reciprocal, -1/n

*If a line is horizontal, slope=0, equation is y=b

*If a line is vertical, slope is not defined, equation is x=a, where a is x-intercept.

*Parallel lines have same slope.

EQUATION:

Equation of a circle is (x - a)^2 + (y-b)^2 = r^2, where (a,b) is the center and r is the radius

Equation of a circle is x^2+y^2=r^2 if (0,0) is the center

Equation of a line is y=mx+b, where m=slope and b=y intercept

* y intercept is the value of y when x is 0
x intercept is the value of x when y is 0

* Points that solve the equation of a line are in the same line

*Given a point and slope, equation of the line can be found

*Given the equation, x and y intercepts can be found

DISTANCE between two points = sqrt[(x1-x2)^2+(y1-y2)^2]

MIDPOINT: xm=(x1+x2)/2 ym=(y1+y2)/2

I know, the properties do not end here. Hope you guys join in.

Last edited by Sumithra on 16 Jan 2007, 12:46, edited 3 times in total.

Would appreciate if someone could shed some light on how to view an equation/inequality in xy-plane, for both straight lines and curves?

For lines, curves or any functions represented on an XY Plan, the concepts remain similar.

o y > f(x) On the XY plan, the matching values of y are "above" the draw of y = f(x).

To know where is the concerned region, u can use 1 value of x : x=0 (if definied on 0), calculate f(0) and then look where is a value of y such that y > f(0). U will be "above" the f(x).

Ex 1 : For the line f(x) = 3*x+1, y > f(x) is in green (fig 1). f(0) = 1 so u know that the point (0,2) is in good region. Now, we can draw the region limited by the line and containing (0,2).

Ex 2 : For the line f(x) = -2*x-1, y > f(x) is in green (fig 2). f(0) = -1 so u know that the point (0,0) is in good region.

Ex 3 : For the line f(x) = x^2 -2*x -1, y > f(x) is in green (fig 3). f(0) = -1 so u know that the point (0,0) is in good region.

o y < f(x) On the XY plan, the matching values of y are "under" the draw of y = f(x).

To know where is the concerned region, u can use 1 value of x : x=0 (if definied on 0), calculate f(0) and then look where is a value of y such that y < f(0). U will be "under" the f(x).

Ex 4 : For the line f(x) = -x+1, y < f(x) is in green (fig 4). f(0) = 1 so u know that the point (0,0) is in good region.

Ex 5 : For the line f(x) = 2*x^2 +4*x -1, y < f(x) is in green (fig 5). f(0) = -1 so u know that the point (0,-2) is in good region.

Attachments

Fig1_y_above_3x+1.gif [ 2.88 KiB | Viewed 13309 times ]

Fig2_y_above_-2x-1.gif [ 2.76 KiB | Viewed 13304 times ]

Fig3_Y_above_Xpow2-2X-1.gif [ 2.66 KiB | Viewed 13303 times ]