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.

Question

Philoid · Accepted Answer

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