A set of transformations that would prove ΔQRS ~ ΔUTS is: A. Reflect ΔUTS over y = 2, and dilate ΔU′T′S′ by a scale factor of 2 from point S.
In Mathematics and Euclidean Geometry, a reflection across the line y = k and y = 2 can be modeled by the following transformation rule:
(x, y) → (x, 2k - y)
(x, y) → (x, 4 - y)
By applying a reflection across the line y = 2 to the coordinates of the pre-image (triangle), we have the following image coordinates;
(x, y) → (x, 4 - y)
Q (-6, 2) → (-6, 4 - 2) = Q' (-6, 2)
Next, we would apply a dilation to ΔU′T′S′ by using a scale factor of 2 centered at point S (-2, 2) ≡ (a, b);
(x, y) → (k(x - a) + a, k(y - b) + b)
Coordinate U' = (-4, 2) → (2(-4 - (-2)) + (-2), 2(2 - 2) + 2)
Coordinate U' = (-4, 2) → (2(-2) - 2, 2(0) + 2)
Coordinate U' = (-4, 2) → (-4 - 2, 0 + 2)
Coordinate U' = (-6, 2).
Missing information:
The question is incomplete and the missing figure is shown in the attached picture.