Step-by-step explanation:
Given a dilation about the origin, with following points
H(-1,3), I(1,1)
H'(-1.4,4.5), I'(1.5,1.5)
Solution:
In the case of dilation about the origin, the scale factor is calculated by the value:
k = X'/X = Y'/Y
where (X,Y) was dilated to form (X', Y').
This relation must be obeyed for ALL the points dilated.
In the given example,
Points H(-1,3), H'(-1.5,4.5):
X=-1, X'=-1.5, k=-1.5/-1 = 1.5
Y=3, Y'=4.5, k= 4.5/3 = 1.5
Points I(1,1), I'(1.5,1.5):
X=1, X'=1.5, k=1.5/1 = 1.5
Y=1, Y'=1.5, k=1.5/1 = 1.5
Since the value of k = 1.5 for all the given points, we can safely conclude that the scale factor is 1.5, or 3/2.
