Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'C'D'. If = 6, what is the scale factor of the dilation?

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Answer:
dilation factor is 2

Explanation:
First, we will need to find the distance of AB as follows:
distance = [tex] \sqrt{(x2 - x1)^2 + (y2 - y1)^2} [/tex]
AB = [tex] \sqrt{(4-1)^2 + (1-1)^2} [/tex]
AB = √9 = 3 units

Dilation can be represented as follows:
A'B' = k * AB
where k is the dilation factor

We are given that:
A'B' = 6

We can note that:
A'B' = 2 * AB
Therefore, the dilation factor is 2.

Hope this helps :)