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

Answer 1

y=-x/3 + b is a perpendicular line through the line segment connecting (1,0) and (2,3)

the line segment has slope = (3-0)/(2-1) = 3/1

the perpendicular line has an inverse negative slope = -1/3

take 3/1, flip it upside down, and change its sign

y=mx+b with m=-1/3,

if the perpendicular line went through (1,0)

the line would be 0=-1/3 +b, and b=1/3

y = -x/3 + 1/3

if the perpendicular line went through (2,3)

the line would be 3 = -2/3 + b

b = 3+2/3 = 11/3

y = -x/3 + 11/3

if the line went between them cutting the line segment in 1/2, it would go through (3/2, 3/2) and

3/2 =-(3/2)/3= -1/2 + b

b = 2 = 6/3

y=-x/3 + 2

it helps to sketch the points and lines

if the line cut the line segment in a ratio of 1/n

it would go through ((n+1)/n, 3/n)

3/n = -((n+1)/n)/3 + b

b = 3/n +(n+1)/3n= 9/3n+(n+1)/3n=(n+10)/3n

y = -x/3 +(n+10)/3n