[R] x, y for point of intersection

[Monica Pisica]

Hi everyone,

 

I am trying to get a point of intersection between a
polyline and a straight line ….. and get the x and y coordinates of this point.
For exemplification consider this:

 

 

set.seed(123)

 

k1 <-rnorm(100, mean=1.77, sd=3.33)

 k1 <- sort(k1)

q1 <- rnorm(100, mean=2.37, sd=0.74)

q1 <- sort(q1, decreasing = TRUE)

plot(k1, q1, xlim <- c((min(k1)-5), (max(k1)+5)),
type="l")

 

ya <- 2

xa = -5

yb=4

xb=12

 

lines(c(xa, xb), c(ya, yb), col = 2)

 

# I want to get the x and y coordinates of the
intersection of the 2 lines ….

 

m <- (ya-yb)/(xa-xb)

b <- ya-m*xa

ln <- loess(q1~k1)

lines(ln)

 

It is clear that the x, y will satisfy both linear
equations, y = m*x + b and the ln polyline ….. but while I can visualize the
equation of the straight line – I have problems with the polyline. I will appreciate
any ideas to solve this problem. I thought it a trivial solution but it seems I
cannot see it.
Thanks,
Monica