I have difficulties to find the proper way to solve the following exercise.
In the swiss grid map we have so called LFPs which are (x,y) anchors. I am looking for a (x,y) position that is 12m further away from LFP 11131157 then the intersection of the line 1 and 2. Also the position is 1285m away from LFP 11128160.
Line 1 = L1 = (LFP 11128119 to LFP 11131157)
Line 2 = L1 = (LFP 11128160 to LFP 11130070)
Some specifications to the LFPs
L1
LFP2 11131157
LV03-Koordinaten (Y / X) 709404.07 / 239148.92
LFP2 11128119
LV03-Koordinaten (Y / X) 706526.64 / 239869.37
L2
LFP 2 11128160
LV03-Coordinates (Y / X) 706943.05 / 238913.67
LFP 2 11130070
LV03-Coordinates (Y / X) 708154.54 / 239929.94
To visualize I have drawn some lines. The point should be somewhere on the blue line between the intersection (green, red line) and LFP 11131157
Calculations
I started calculating the intersection.
$ L1 = \binom{239869.37}{709404.07} + r\binom{720.45}{-2877.43} \\ L2 = \binom{238913.67}{706943.05} + s\binom{1016.27}{1211.49} $
Intersection $S$
$ L1 = L2 \\ 239148.92 + 720.45r = 238913.67 + 1016.27s \\ 709404.07 - 2877.43r = 706943.05 + 1211.49s $
Which gives
$S = (239569.3919, 707724.7326)$
Distance $D$ between $S$ and $LFP 11131157$
$D = \sqrt{(239569.3919-239148.92)^2 + (707724.7326-709404.07)^2} = 1731$ meter
What would be the next step from here?