Question

A line through through the point (3,0) meet the variable line y=tx at right angle at the point P.
Find in terms of t, the co-ordinates of P

Answer 1

P has coordinates (x,tx)
The line from (3,0) to P has slope -1/t

now, drop an altitude from P to the x-axis.

tx/(x-3) = -1/t
x = 3/(1+t^2)

P = (3/(1+t^2), 3t/(1+t^2))

Answer 2

line 1: y=tx
line 2: y=-x/t +b
but you know point 3,0 is on line 2
0=-3/t + b or b=3/t
line2: y=-x/t +3/t
line1 y=tx
set them equal
tx=-x/t+3/t solve for x
then solve for y.

Answer 3

Thank u so much @steve and @bobpursley