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