Use the image to answer the question.
A coordinate grid of quadrant 1 shows 2 plotted triangles of the same shape but different sizes. The x and y axes range from 0 to 10 in unit increments. A small tilted triangle upper A upper B upper C is formed by connecting the following plots: point upper A is left parenthesis 2 comma 1 right parenthesis; point upper B is left parenthesis 3 comma 2 right parenthesis; and point upper C is left parenthesis 1 comma 3 right parenthesis. A large tilted dotted triangle is formed by connecting the following plots: point upper A prime is left parenthesis 6 comma 3 right parenthesis; point upper B prime is left parenthesis 9 comma 6 right parenthesis; point upper C prime is left parenthesis 3 comma 9 right parenthesis.
What is the scale factor of a single dilation between the preimage ABC and image A′B′C′ ?
(1 point)
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The scale factor of a dilation is found by comparing the corresponding side lengths of the preimage and the image.
In the given figure, the side lengths of triangle ABC are AB = 1, BC = 1, and CA = 2.
The side lengths of triangle A'B'C' are A'B' = 3, B'C' = 3, and C'A' = 6.
To find the scale factor, divide the corresponding side lengths of the image by the corresponding side lengths of the preimage.
Scale factor = A'B' / AB = 3 / 1 = 3
Therefore, the scale factor of a single dilation between the preimage ABC and image A'B'C' is 3. Answer: \boxed{3}.