Enlargement

This file illustrates a general enlargement without and with a centre of enlargement.

Method 1

Method 2

Areas

Condition

A = (0, 0)
B = (0, 3)
C = (1, 3)
D = (1, 2)
E = (2, 1)
F = (1, 0)
poly1, a, b, c, d, e, f = Polygon(A, B, C, D, E, F)
O = (-3, 1)
H = (3, 0)
ScaleFactor = 3 (slider from 0 to 4, step 0.1)
A' = Dilate(A, ScaleFactor, O)
B' = Dilate(B, ScaleFactor, O)
C' = Dilate(C, ScaleFactor, O)
D' = Dilate(D, ScaleFactor, O)
E' = Dilate(E, ScaleFactor, O)
F' = Dilate(F, ScaleFactor, O)
poly1', a', b', c', d', e', f' = Polygon(A', B', C', D', E', F')
g = Ray(O, B)
h = Ray(O, A)
i = false
u = Vector(A, B)
v = Vector(B, C)
w = Vector(C, D)
z = Vector(D, E)
j = Vector(E, F)
l = Vector(F, A)
H' = Translate(H, Vector[ScaleFactor * u])
H'' = Translate(H', Vector[ScaleFactor * v])
n = Vector(H', H'')
H''' = Translate(H'', Vector[ScaleFactor * w])
p = Vector(H'', H''')
G = Translate(H''', Vector[ScaleFactor * z])
q = Vector(H''', G)
G' = Translate(G, Vector[ScaleFactor * j])
r = Vector(G, G')
G'' = Translate(G', Vector[ScaleFactor * l])
s = Vector(G', G'')
m = Vector(H, H')
poly2, h_1, h', h'', h''', g_1, g' = Polygon(H, H', H'', H''', G, G')
o = true
DivArea: poly1' / poly1
text1: "\frac{Transformed \;  Image}{Original \; Image} = \frac{" + (LaTeX[poly1']) + "}{" + (LaTeX[poly1]) + "} = " + (LaTeX[DivArea]) + " = (" + (LaTeX[ScaleFactor]) + ")^2"
t = false
text2: "Original Area = " + poly1 + ""
text3: "Transformed Area = " + poly1' + ""
a_1 = false