# A problem. Find the intersection point. A = 45+30 # (y--2)=k(x-1) line (1,-2)-? f = function(x) k*(x-1)-2 k = tan(A/180*pi) # The intersection of y=x and y=f(x): F = function(x) f(x)-x; x1 = solution(F,0, 1,3); x1 # 2.098076 # "?" is the point (2.098076, 2.098076) # # How the figure was built: BF=2.6; HF=2.6 PLANE(-1.5,4, -3,2.5) abline(0,1, col="seagreen",lwd=2) POINT(1,-2, "brown") text(0.5,1.5,"y=x") text(1.5,-2.5,"(1,-2)",cex=0.8) graph2(f, -2,5, "seagreen") POINT(x1,x1, "brown") ARC(x1,x1, 1, 225,atan(k)*180/pi+180, "seagreen") text(2.4,1.5,"30^",cex=0.8) text(1.6,2.3,"?",font=2) # line(1,-2, 4,-2, "brown") text(1.6,-1.5,"A^") text(2.7,-0.7,"y=k*(x-1)-2",cex=0.8)