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

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

Formula to be used: If (a,b) and (c,d) are two points then the equation of the line passing through them is

If (a₁,b₁) and (a₂,b₂) be two points , then the co - ordinates of the point dividing their join in the ratio a:b is given by

The equation of the line joining points (1,0) and (2,3) is

or,

i.e. the given line is 3x - y = 3.

Accordingly, the required co - ordinates of the point dividing the join of (1,0) and (2,3) in the ratio 1:2 are

The given line is 3x - y = 3.

The slope of this line is .

the slope of the perpendicular line =

The equation of the line can be written in the form

(c is the y - intercept)

This line will pass through .

The required equation is

i.e. 3x + 9y = 13