x

b

x

What is the area of the purple square in terms of x?
What is the area of the blue rectangle in terms of b and x?
Use the sliders in order.
Explain.

1

2

A = (-3.154, 3.818)
a = OrthogonalLine(A, yAxis)
B = Point(a)
ray1 = Ray(A, B)
C = Point(ray1)
b = Segment(A, C)
ray2 = Ray(C, B)
D = Point(ray2)
c = Segment(C, D)
d = OrthogonalLine(A, b)
e = Circle(A, C)
E = Intersect(e, d, 1)
f = OrthogonalLine(C, b)
g = OrthogonalLine(E, d)
F = Intersect(f, g)
h = OrthogonalLine(D, c)
G = Intersect(g, h)
poly1, a_1, e_1, f_1, c_1 = Polygon(A, E, F, C)
poly2, c_2, d_1, g_1, f_2 = Polygon(C, D, G, F)
H = Midpoint(c)
I = Midpoint(g_1)
poly3, f_3, i, h_1, c_3 = Polygon(F, I, H, C)
j = Line(A, F)
F' = Mirror(F, j)
I' = Mirror(I, j)
H' = Mirror(H, j)
C' = Mirror(C, j)
k = 0 (slider from 0 to 90, step 0.5)
l = LineBisector(E, I)
m = LineBisector(H, F)
J = Intersect(l, m)
poly4, h_2, d_2, g_2, i_1 = Polygon(H, D, G, I)
H'_1 = Rotate(H, (-(k°)), J)
D' = Rotate(D, (-(k°)), J)
G' = Rotate(G, (-(k°)), J)
I'_1 = Rotate(I, (-(k°)), J)
poly4', h'_1, d', g', i'_1 = Polygon(H'_1, D', G', I'_1)
n = Line(H', I')
L = Intersect(j, n)
o = 0 (slider from 0 to 1, step 0.05)
L' = Dilate(L, o, F)
p = OrthogonalLine(L', c)
K = Intersect(p, g_1)
q = OrthogonalLine(L', f)
M = Intersect(f, q)
poly5, m_1, f_4, k_1, l' = Polygon(M, F, K, L')