Question

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

Answer 1

The slop of the line joining A(1, 0) and B(2,3) is
$\frac{3 - 0}{2 - 1} = 3$
and the coordinates of the point dividing it in the ratio 1:n are

{(n+2/n+1), (3/n+1)}.

The slop of the line perpendicular to the line segment AB is

$\frac{ - 1}{3}$
Hence the equation of the required line is

$y - \frac{3}{n + 1} = - \frac{1}{3}(x - \frac{n + 2}{n + 1}) \\ \\ or \: \: (n + 1)y - 3 = \frac{ -1 }{3} (x(n + 1) - (n + 2)) \\ \\or \: \: 3(n + 1)y - 9 = - x(n + 1) + (n + 2) \\ \\or \: \: (n + 1)x + 3(n + 1)y = n + 2 + 9 \\ \\ or \: \: (n + 1)x + 3(n + 1)y = n + 11$


Hope it helps.....

Answer 2

hey mate ‼️‼️‼️

ur solution is in the attachment ⤴️⤴️

✌✌hope its help you ✌✌

thank you ♠️♠️❤❤