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 b 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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