Question

Which set of transformations would prove Δqrs Δuts?

1) a reflect Δuts over y = 2, and dilate Δu²t²s² by a scale factor of 2 from point s.
2) reflect Δuts over y = 2, and translate Δu²t²s² by the rule (x 2, y 0).
3) translate Δuts by the rule (x 0, y 6), and reflect Δu²t²s² over y = 6.
4) translate Δuts by the rule (x - 2, y 0), and reflect Δu²t²s² over y = 2.

Answer 1

To prove that triangles ∆qrs and ∆uts are congruent, you should translate ∆uts by (x 0, y +6) and then reflect it over the horizontal line y = 6. This series of transformations will superpose one triangle onto the other without changing its size or shape, demonstrating congruency.

Step-by-step explanation:

The student's question is about proving that two triangles, ∆qrs and ∆uts, are congruent through a series of transformations. The correct set of transformations needed to prove ∆qrs is congruent to ∆uts would involve steps that superpose one triangle onto the other without altering its size or shape, as congruent figures are identical in form and dimensions.

Option 3) is the correct answer. By translating ∆uts by the rule (x 0, y +6), we move ∆uts six units up on the coordinate plane. Then, by reflecting ∆u²t²s² over the horizontal line y = 6, we get an image that is congruent to the original ∆qrs. These transformations would successfully demonstrate that ∆qrs is congruent to ∆uts, assuming that the initial and transformed positions, as well as orientations of the triangles, are compatible.