# A line perpendicular to the linesegment joining the points(1, 0) and (2, 3) divides it in the ratio 1 : n. Find the equation of the line.

A line l with A(1, 0) and B(2, 3) as end points is given

l ⊥ AB and AC : CB = 1 : n Now coordinates of C are or which is C.

Now slope of AB = = 3

Now slope of l = - (as m1m2 = -1)

equation of l is:

y – y1 = n(x – x1)

or y- = 3 = - 3(n + 1)y – 9n = -(n + 1)x + (n+2)

(1 + n)x + 3(1 + n)y = 10n + 2

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