Determine a similarity transformation that maps the primage to the image.

Step-by-step explanation:

From the figure attached,

ΔABC has been dilated to form another triangle ΔA'B'C'.

Therefore, ΔA'B'C' is the image triangle of preimage ΔABC.

Coordinates of preimage ΔABC are,

A(3, 3), B(2, 0) and C(5, 2)

Coordinates of ΔA'B'C',

A'(6, 6), B'(0, 4) and C'(10, 4)

Since, dilation of a triangle is a similarity transformation which produces the  similar image of the preimage.

Rule for the dilation is,

(x, y) → (kx, ky)

Here, k = scale factor of dilation

By this rule,

A(3, 3) → A'(6, 6)

          → A'(2×3, 2×3)

Scale factor = 2

Therefore, "Triangle (ABC) is dilated by a scale factor 2 about the origin to form triangle (A'B'C') ".