2. Determine the scale factor used in the dilation of line segment AB, centered at the origin. A (2,3) to B (4,1) and A' (6,9) to B' (12,3)
To determine the scale factor used in the dilation of the line segment AB, we can calculate the ratio of the corresponding side lengths.
The length of line segment AB is given by the distance formula:
√((4-2)^2 + (1-3)^2) = √(2^2 + (-2)^2) = √(4 + 4) = √8 ≈ 2.83
The length of line segment A'B' is also given by the distance formula:
√((12-6)^2 + (3-9)^2) = √(6^2 + (-6)^2) = √(36 + 36) = √72 ≈ 8.49
The scale factor, k, can be calculated by dividing the length of A'B' by the length of AB:
k = √72 / √8 ≈ 8.49 / 2.83 ≈ 3
Therefore, the scale factor used in the dilation of line segment AB is 3.