Question

determine the scale factor used in the dilation of line segment AB, with a center point of dilation at origin.

A(9,9)
B(6,6)

A'(3,3)
B'(2,2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the scale factor used in the dilation of line segment AB with a center point of dilation at the origin, we can calculate the distance between the points A and B and the distance between the points A' and B'.

The distance between points A and B using the distance formula is:
AB = √[(9-6)^2 + (9-6)^2]
AB = √[3^2 + 3^2]
AB = √(18)
AB ≈ 4.24

Similarly, the distance between points A' and B' is:
A'B' = √[(3-2)^2 + (3-2)^2]
A'B' = √[1^2 + 1^2]
A'B' = √(2)
A'B' ≈ 1.41

The scale factor is the ratio of the length of the image to the length of the pre-image:
Scale factor = A'B' / AB
Scale factor = 1.41 / 4.24
Scale factor ≈ 0.3333

Therefore, the scale factor used in the dilation of line segment AB with a center point of dilation at the origin is approximately 0.3333.