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Question

Summarize the chapter of straight lines with the different formulas?


Solution

Consider two points P(x1,y1)P(x1,y1) and Q(x2,y2)Q(x2,y2), then:

distance formulaPQ=x2-x12+y2-y12midpoint formula=x1+x22,y1+y22point Rx,y divides PQ  in the ratio k1k2k1x2+k2x1k1+k2,k1y2+k2y1k1+k2slope of PQm=y2-y1x2-x1slope of x axis or line parallel to x axis is zeroslope of y axis is not defined ie infinity
​​

The equation of the x-axis is y=0

 The equation of the x-axis is x=0

 The equation of the line parallel to the x-axis and at a distance a is y=a

T​​​​​he equation of the line parallel to the y-axis and at a distance b is x=b

1The equation of the line with slope mm and y-intercept cc is y=mx+c, which is called the slope – intercept form.

The equation of the line passing through (x1,y1)(x1,y1) and having the slope m is y−y1=m(x−x1), which is called the slope – point form
The equation of the line passing through two points (x1,y1) and (x2,y2) is

y-y1y2-y1=x-x1x2-x1



The equation of the line having   
a
and
as the x – intercept and y – intercept is 





xa+yb=1
and is called the equation of the line in intercept form.

. The normal form of the straight line is
xcos⁡α+ysin⁡α=p
, where
p
is the length of the perpendicular from
O(0,0)
to the line, and
α
is the inclination of the perpendicular


 

The general form of the equation of a straight line is ax+by+c=0. Consider two lines l1 and l2 having the slopes m1 and m2, respectively.

​​​​​​If two lines l1 and l2 are parallel, then m1=m2

If two lines l1 and l2 are parallel, then m1×m2=−1


 




 

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