Find the ratio in which the line segment joining the points (-3,10)and

1.	Find the ratio in which the line segment joining the points (-3,10)and (6,-8)is divided by (-1,6)
Answer» Here x₁ = -3, y₁ = 10, x₂ = 6, y₂ = -8 ...... [m(6) + n (-3)]/(m+n) ,\xa0[m (-8) + n (10)]/(m+n) = (-1,6)\xa0....... (6m - 3n)/(m+n), (-8m+10n)/(m+n) = (-1,6) .......\xa0equating the coefficients of x and y....... (6m-3n)/(m+n) = -1 ....... (-8m+10n)/(m+n) = 6........... 6m - 3n = -1 (m+n)............ 6m - 3n = -1 (m+n).......... 6m-3n=-m-n.......... 6m+m=-n+3n......... 7m=2n.. ......... m/n= 2/7......... m:n = 2:7..........So the point (-1,6) is dividing the line segment in the ratio 2:7. Let P(-1, 6) divides the line segment joining the points A(-3, 10) and B(6, -8) in the ratio K : 1.Then the co-ordinates of P are given byHere, we havex1\xa0= -3, y1\xa0= 10x2\xa0= 6, y2\xa0= -8and m1\xa0= K, m2\xa0= 1So, the co-ordinates of P areBut the co-ordinates of P are given as P(-1, 6)Hence, required ratio = 2 : 7.

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