# The line at a point `p` parallel to the line segment joining two distinct 2D points `a` and `b` An object of class `"Lines"`. Returns the `equation, slope, intercept`, and $y$-coordinates of the line crossing the point `p` and parallel to the line passing through the points `a` and `b` with $x$-coordinates are provided in `vector` `x`. ```r paraline(p, a, b, x) ``` ## Arguments - `p`: A 2D point at which the parallel line to line segment joining `a` and `b` crosses. - `a, b`: 2D points that determine the line segment (the line will be parallel to this line segment). - `x`: A scalar or a `vector` of scalars representing the $x$-coordinates of the line parallel to `ab` and crossing `p`. ## Returns A `list` with the elements - **desc**: Description of the line passing through point `p` and parallel to line segment joining `a` and `b` - **mtitle**: The `"main"` title for the plot of the line passing through point `p` and parallel to line segment joining `a` and `b` - **points**: The input points `p`, `a`, and `b` (stacked row-wise, i.e., point `p` is in row 1, point `a` is in row 2 and point `b` is in row 3). Line parallel to `ab` crosses p. - **x**: The input vector. It can be a scalar or a `vector` of scalars, which constitute the $x$-coordinates of the point(s) of interest on the line passing through point `p` and parallel to line segment joining `a` and `b`. - **y**: The output scalar or `vector` which constitutes the $y$-coordinates of the point(s) of interest on the line passing through point `p` and parallel to line segment joining `a` and `b`. If `x` is a scalar, then `y` will be a scalar and if `x` is a `vector` of scalars, then `y` will be a `vector` of scalars. - **slope**: Slope of the line, `Inf` is allowed, passing through point `p` and parallel to line segment joining `a` and `b` - **intercept**: Intercept of the line passing through point `p` and parallel to line segment joining `a` and `b` - **equation**: Equation of the line passing through point `p` and parallel to line segment joining `a` and `b` ## Examples ```r A<-c(1.1,1.2); B<-c(2.3,3.4); p<-c(.51,2.5) paraline(p,A,B,.45) pts<-rbind(A,B,p) xr<-range(pts[,1]) xf<-(xr[2]-xr[1])*.25 #how far to go at the lower and upper ends in the x-coordinate x<-seq(xr[1]-xf,xr[2]+xf,l=5) #try also l=10, 20, or 100 plnAB<-paraline(p,A,B,x) plnAB summary(plnAB) plot(plnAB) y<-plnAB$y Xlim<-range(x,pts[,1]) if (!is.na(y[1])) {Ylim<-range(y,pts[,2])} else {Ylim<-range(pts[,2])} xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] pf<-c(xd,-yd)*.025 plot(A,pch=".",xlab="",ylab="",main="Line Crossing P and Parallel to AB", xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) points(pts) txt.str<-c("A","B","p") text(pts+rbind(pf,pf,pf),txt.str) segments(A[1],A[2],B[1],B[2],lty=2) if (!is.na(y[1])) {lines(x,y,type="l",lty=1,xlim=Xlim,ylim=Ylim)} else {abline(v=p[1])} tx<-(A[1]+B[1])/2; if (!is.na(y[1])) {ty<-paraline(p,A,B,tx)$y} else {ty=p[2]} text(tx,ty,"line parallel to AB\n and crossing p") ``` ## See Also `slope`, `Line`, and `perpline`, `line` in the generic `stats` package, and `paraline3D` ## Author(s) Elvan Ceyhan

paraline function