Question

Determine the scale factor used in the dilation of line segment AB , centered at the origin. A (2,3), B (4,1) A' (6,9) B' (12,3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the scale factor in the dilation of line segment AB centered at the origin, we can compare the distance between points A and B to the distance between points A' and B'.

The distance between points A and B is calculated using the distance formula, which is √((x2-x1)^2 + (y2-y1)^2):
√((4-2)^2 + (1-3)^2) = √(2^2 + (-2)^2) = √(4 + 4) = √8

The distance between points A' and B' is also calculated using the distance formula:
√((12-6)^2 + (3-9)^2) = √(6^2 + (-6)^2) = √(36 + 36) = √72

Thus, the scale factor is the ratio of the distance between A' and B' to the distance between A and B: √72/√8.

Simplifying the expression, we get:
(√72/√8) = (√(8*9)/√8) = (√8 * √9)/√8 = 3

Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 3.