Question

Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these transformations, which statement is true?

coordinate plane with triangles ACB and XYZ with A at negative 4 comma 4, C at negative 1 comma 3, B at negative 4 comma 0, X at 0 comma 8, Y at 8, comma 8, and Z at 6 comma 2

∠B ≅ ∠X
∠A ≅ ∠Z
∠C ≅ ∠X
∠Y ≅ ∠B

Answer 1

The rotation and dilation from Triangle BAC to Triangle XYZ preserve angle measures, so angle B is congruent to angle X. The correct answer is option: ∠B ≅ ∠X

Step-by-step explanation:

When Triangle BAC is rotated 90° clockwise and dilated by a scale factor of 2 from the origin to create Triangle XYZ, the angles at the corresponding points maintain their measures due to the properties of rotations and dilations.

A rotation preserves the angles' measures, and a dilation scales the size but does not change the angle measures.

Therefore, since the rotation is from B to X, and X corresponds to B after these transformations, the correct answer is ∠B ≅ ∠X.