Question

Find the equation of the line through (2,3) so that the segment of the line intercepted between the axes is bisected at this point.

Answer 1

Let AB be the given line segment making intercepts a and b on the x-axis and y-axis respectively. Then, the equation of line AB is `(x)/(a)+(y)/(b)=1`
Morever, these points are A(a,0) and B(0,b). Let M(2,3) be the midpoint of AB. Then, `(a+0)/(2)=2 and (0+b)/(2)=3`
`Rightarrow a=4 and b=6`
Hence, the required equation of the given line is
`(x)/(4)+(y)/(6)=1 Leftrightarrow 3x+2y-12=0`
Hence, the required equation is 3x+2y-12=0