Do you know the formula for the distance from a point to a line, i.e., the length of perpendicular in this case?
I am not able to solve this problem of Book 'The Element of Co-ordinate of SL Loney'
Find the equations of the two straight lines drawn through
the point (0, a) on which the perpendiculars let fall from the point
(2a, 2a) are each of length a.
Thanx in advance
Find the equations of the two straight lines drawn through A(0,a)
on which the perpendiculars from the point B(2a,2a) are each of length a.We have: ∆ABC: AC = 2a, BC = a.Code:| D | * | / * a | 2a / * B | / *(2a,2a) | / * : | / * :a A |/@ * @ : (0,a)* - - - - - - - * - - | 2a :C | : | : - - * - - - + - - - + - - - | a 2a |
We see that one line is: .y = a
Reflect ∆ABC over AB so that: ∆ABD ≅ ∆ABC.
Let θ = /BAC = /BAD.
The slope of AB is: .tanθ = 1/2
. . . . . . . . 2tanθ . . . . . .2(1/2) . . . . .1 . . . . 4
tan2θ .= .----------- .= .---------- .= .---- .= .--
. . . . . . . .1 - tan2θ . . . 1 - (1/2)2 . . .3/4 . . . 3
The other line is: .y = (4/3)x + a