Question

Coordinate plane with triangles qrs and uts with q at negative 6 comma 2, r at negative 2 comma 6, s at negative 2 comma 2, t at negative 2 comma 0, and u at negative 4 comma 2 which set of transformations would prove δqrs ~ δuts? group of answer choices reflect δuts over y = 2, and dilate δu′t′s′ by a scale factor of 2 from point s. reflect δuts over y = 2, and translate δu′t′s′ by the rule (x − 2, y 0). translate δuts by the rule (x 0, y 6), and reflect δu′t′s′ over y = 6. translate δuts by the rule (x − 2, y 0), and reflect δu′t′s′ over y = 2.

Answer 1

The correct transformation to demonstrate that ∆QRS is similar to ∆UTS is to reflect ∆UTS over y=2, followed by a translation using the rule (x - 2, y + 0).

Step-by-step explanation:

To determine which set of transformations proves that ∆QRS is similar to ∆UTS, we first look at the coordinates provided for the vertices of both triangles. The triangles' coordinates suggest certain geometric transformations that could be executed to demonstrate similarity. Considering the transformations and the given coordinates, the correct sequence of transformations involves a reflection followed by a translation or dilation.

The option 'reflect ∆UTS over y = 2, and translate ∆U'T'S' by the rule (x - 2, y + 0)' allows triangle UTS to be reflected across the line y=2, and then translated left by 2 units, aligning it with ∆QRS and demonstrating that both triangles are similar through reflection and translation.