State the scale factor of the dilation about the origin of these coordinates.

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.