# 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)