In what ratio does the line x-y-2=0 divide the line joining the points

1.	In what ratio does the line x-y-2=0 divide the line joining the points A(3,-1) and B(8,9)?
Answer» Let the ratio be k : 1.The given points are A(3, -1) and B(8, 9).Then the coordinates of point of intersection are: m1x2+m2x1m1+m2,m1y2+m2y1m1+m2 = k×8+1×3k+1,\xa0k×9+1×-1k+1 = 8k+3k+1,\xa09k-1k+1Now, these coordinates is on the line x - y - 2 = 0Then putting the coordinates of intersection point in this line, we get8k+3k+1-9k-1k+1-2=0=> 8k+3-9k+1-2k-2=0=> -3k+2=0=> k=23Therefore, the required ratio is 2 : 3.

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