I would like to coin together certain properties of

Question

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 

 MIDPOINT : xm=(x1+x2)/2 ym=(y1+y2)/2

I know, the properties do not end here. Hope you guys join in.

Sumithra · Answer

Thank you tennis ball. Edited my previous post.

Can somebody explain 'functions'?

Sumithra · Answer

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

Fig · Answer

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.

Fig · Answer

Fig 4 and 5

svas · Answer

hey things like distance between (a,b) (c,d) : its a right angle triangle. simple pythagoras formula that is applied there.

all who gave gmat already, Did you try to remember all of these ? I am trying to rely on doing these right there. am i being over-ambitious ?

Sumithra · Answer

Thanks Fig for taking pains to explain. Now, I understand better.

Dr MBA · Answer

wow.... all tis stuff is great... made my day.......... hopefully also my GMAT


Better to understand a little than to misunderstand a lot

beckee529 · Answer

Thanks for putting in the time to provide this guide, this will be very helpful with my studies!

getbig · Answer

thanks for the collection of formulas... I've been looking for something like this.

Ibodullo · Answer

Thanks for that one!

irajeevsingh · Answer

Thanks for collating it at one place.

amit2k9 · Answer

thanks for the approach.However,Can somebody please explain me how to plot,
 y>f(x),where f(x) = x^2-2x -1.

Thanks in advance.

Bunuel · Answer

Plot y=x^2-2x-1. y>x^2-2x-1 would be above the graph: MSP5724200423hdf0492bch00005382e4a5b3eah3fg.gif Does this make sense?

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I would like to coin together certain properties of

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