To find the scale factor of the dilation, we can compare the lengths of corresponding sides of the original and dilated triangles.
The distance between points A (-2,4) and B (-6,8) can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2)
So the distance between A and B is √((-6 - (-2))^2 + (8 - 4)^2) = √((-4)^2 + 4^2) = √(16 + 16) = √32 = 4√2.
The distance between points A' (-1,2) and B' (-3,4) can also be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2)
So the distance between A' and B' is √((-3 - (-1))^2 + (4 - 2)^2) = √((-2)^2 + 2^2) = √(4 + 4) = √8 = 2√2.
To find the scale factor, we can divide the length of the corresponding side in the dilated triangle by the length of the corresponding side in the original triangle: (2√2) / (4√2) = 1/2
Therefore, the scale factor for the dilation of triangle ABC is 1/2.
The correct answer is a. 1/2.