Triangle ABC has vertices A(4,8) B(-3,2) and C(-1,6). Triangle ABC is dilated so that the new vertices are A'(12,24) B'(-9,6) and C'(-3,18). What is the scale factor?
Answers
Answer:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
Note: A dilation is NOT referred to as a rigid transformation (or isometry) because the image is NOT necessarily the same size as the pre-image (and rigid transformations preserve length).
Referring to the diagram below:
The dilation (centered at O with a scale factor of 2) of ΔABC = ΔA'B'C' making ΔABC ∼ ΔA'B'C' .
This could also be written if you consider ΔABC to be the image.
