I have 2 parallel lines which are touching a rectangle.
I know the coordinates (x1,y1), (x2,y2), (x3,y3), (x4,y4)
How can I find from that the orthogonal distance between the lines?
Asked
Active
Viewed 98 times
0
lio
- 103
-
4Firstly, actually you need to know only three points coordinates. Secondly, think about equations of these lines. Thirdly, think how the orthogonal vector coordinates are connected with line equations. – Denis Korzhenkov Oct 17 '16 at 10:43
1 Answers
0
Let’s make this question a bit harder by finding the d in the following picture.
It is sufficient if we can find h and k, the co-ordinates of T.
T lies on the circle $\omega$ (with PS as diameter), whose equation is $$\omega : (x – x_1)(x – x_4) + (y – y_1)(y – y_4) = 0$$
∴ $(h – x_1)(h – x_4) + (k – y_1)(k – y_4) = 0$ …. (1)
T is also on L and hence $k – y_3 = \dfrac {y_4 – y_3 }{x_4 – x_3}(h – x_3)$ … (2)
Solving (1) & (2) will give us h and k.
Method #2
Use R and S to get the equation of L.
Use P, via the the perpendicular distance formula, to get d.
