The coordinates of the triangle and the list of statements to choose which one is true are:
Triangle ACB:
Ttriangle XYZ:
Statements:
Answer:
- <u><em>∠ A ≅ ∠ Y</em></u>
Explanation:
A<em> rotation 90° clockwise</em> is the same that a rotation 270° counter-clockwise.
The rule for this transformation is:
Thus, applying that rule to the vertices A, C, and B you get:
The second transformation is a <em>dilation with a scale factor of 2</em> <em>from the origin</em>. The rule for this transformation is:
Applying that rule to the vertices A', C', and B', you get:
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.