Question

Aline perpendicular to tha line segment joining tha point (1,0)and(2,3) divides it in tha ratio 1:n find tha equation of tha line.

Answer 1

First, we will use section formula to find the point of intersection of the two lines.
X = (1 + 2n) / (1 + n)
Y = (3n) / (1 + n)
Equation of line passing through (1,0) and (2,3) is y-0 = [(3-0)/(2-1)] ×(x-1)
I.e y = 3x - 3.
Eq. Of line perpendicular to this line is...
y = -x/3 + c.
Since it passes through (X, Y)...
3n/1+n = -[(1+2n) /(1+n)]/3 +c
c = (1/3)(11n +1)/(1+n).
Substitute this in the equation... You will get the answer...
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