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​

Answer 1

The coordinates of the triangle and the list of statements to choose which one is true are:

Triangle ACB:

• A (- 4, 4)

• C (-1, 3)

• B (- 4, 0)

Ttriangle XYZ:

• X (0, 8)

• Y (8, 8)

• Z (6,2)

Statements:

• ∠C ≅ ∠X

• ∠C ≅ ∠Y

• ∠A ≅ ∠Y

• ∠A ≅ ∠X

Answer:

• ∠ A ≅ ∠ Y

Explanation:

A rotation 90° clockwise is the same that a rotation 270° counter-clockwise.

The rule for this transformation is:

• (x, y) → (y, -x)

Thus, applying that rule to the vertices A, C, and B you get:

• A (- 4, 4) → A' (4, 4)

• C (-1, 3) → C' (3, 1)

• B (- 4, 0) → B' (0, 4)

The second transformation is a dilation with a scale factor of 2 from the origin. The rule for this transformation is:

• (x, y) → (2x, 2y)

Applying that rule to the vertices A', C', and B', you get:

• A' (4, 4) → A'' (8, 8)

• C' (3, 1) → C'' (6,2)

• B' (0, 4) → B'' (0, 8)

To compare the two triangles BAC and XYZ, you must keep the order of the letters:

• B was transformed to X, so the coordinates of X are those of B'': (0,8).
• A was transformed to Y, so the coordinates of Y are those of A'': (8, 8)
• C was transformed to Z, so the coordinates of Z are those of C'': (6,2).

The rotation is a rigid transformation, so both lengths and angles were preserved.

Dilation is not a rigid transformatio, because lengths are not preserved, nevertheless angles are preserved.

Hence, the corresponding angles were preserved:

• ∠ B ≅ ∠ X
• ∠ A ≅ ∠ Y
• ∠ C ≅ ∠ Z

Therefore, from the choices, the only true statement is ∠A ≅ ∠Y.

Answer 2

Answer:

The answer is the third option #lol

Step-by-step explanation:

it's because it's a 90degree rotation