Mathematics Geometry

Question

A line perpendicular to the line segment joining the points A (1,0) & B (2,3) divides it at C in the ratio of 1 : 3 . Then equation of the line is.?

Answer 1

The line joining the points A ->(1,0) and B->(2,3) is divided at C in the ratio 1:3. So the coordinates of C will be. ((1×3+2×1)/4,(0×3+3×1))/4)

=(5/4,3/4)

The slope of AB = (3-0)/(2-1)=3

The slope of the line perpendicular to AB will be -1/3

Hence the equation of the line passing through C and perpendicular to AB will be

(y-3/4)-1/3(x-5/4)

=>-12x+15=4y-3

=>12x+4y-18=0