Question

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

Answer 1

Answer:

$y = - \frac{1}{3} x +\frac{11+n}{3(1+n)}$

Step-by-step explanation:

The line passing through the points (1,0) and (2,3) is represented by

$y-0 = \frac{3-0}{2-1}* (x-1)$

y=3(x-1) => y = 3x-3

The slope of the given line is 3.

The slope of the line perpendicular to this line is (-1/3).

The point which divides the line in 1:n is given by the section formula,

$(\frac{2+n}{1+n},\frac{3}{1+n})$

So, the required line must have a slope (-1/3) and should pass through the above point.

So, we have

y=-(1/3)x+c

$(\frac{2+n}{1+n},\frac{3}{1+n})$ lies on the above line.

Substituting it, we have

$\frac{3}{1+n} = \frac{-1}{3} * \frac{2+n}{1+n} + c \\\\</p><p>c= \frac{3}{1+n}+\frac{2+n}{3(1+n)} \\ \\</p><p>c = \frac{9+2+n}{3(1+n)}} = \frac{11+n}{3(1+n)}$

Substituting the value of c in the equation of line we have

$y = - \frac{1}{3} x +\frac{11+n}{3(1+n)}$

Answer 2

this is the solution hope this will help u.....