@above Use Simple Mathematics What is collinear Point...?? what is condition of collinearity..?? thats it You have done
Three or more points P1, P2, P3, ..., are said to be collinear if they lie on a single straight line L similarly for N Points .. Let us start from the Very Basic Mathematical Approach Since any 2 points determine 1 line, take 2 of the points and find the equation of the line drawn thru these 2 points. Substitute the x and y of the either point into the equation and find the y-intercept (b) Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are =. (y2-y1) ÷ (x2 - x1) = slope y = slope * x + b Point # 1 = (6, 5)=p1 Point # 2 = (10, 25)=p1 Point # 3 = (12, 30)=p1 Point # 4 = (12, 35)=p1 (y2 - y1) ÷ (x2 - x1) = slope (25 - 5) ÷ (10 - 6) = slope (20) ÷ (4) = slope Slope = 5 y = m * x + b y = 5 * x + b Substitute the x and y of the point (6, 5) into the equation and find the y-intercept (b) y = 5 * x + b 5 = 5 * 6 + b 5 = 30 + b b = -25 y = 5 * x - 25 . Check your points Point # 1 = (6, 5) 5 = 5 * 6 - 25 5 = 30 - 25 OK . Point # 2 = (10, 25) 25 = 5 * 10 - 25 25 = 5 * 10 - 25 OK . Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are Point # 3 = (12, 30) . y = 5 * x - 25 30 = 5 * 12 - 25 30 = 60 - 25 = 35 Point # 3 = (12, 30) is not on the line . . Point # 4 = (12, 35) 35 = 5 * 12 - 25 35 = 60 - 25 =35 Point # 4 = (12, 35) is on the line so we can p1,p2,p4 are Collinear 2nd Appraoch Used by Actual Geeks as we Two points are trivially collinear since two points determine a line. Three points x_i=(xi,yi,zi) for i=1, 2, 3 are collinear if the ratios of distances satisfy x2-x1:y2-y1:z2-z1=x3-x1:y3-y1:z3-z1 A slightly more notice that the area of a triangle determined by three points will be zero iff they are collinear (including the degenerate cases of two or all three points being concurrent), i.e., | x1 y1 1 | | x2 y2 1 |=0 | x3 y3 1 | or, in expanded form, x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0 Still If You Have the Doubt Let Me Know & if Any found that anything wrong in this..please write correct & efficient ways to do it. Thanks & Regards Shashank ""The best way to escape from a problem is to solve it." . . -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
