Answered

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 :

Edufirst

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.

ankitprmr2

Answer:

Only one Statement is True : [tex]\rm \angle A\cong \angle Y[/tex]

Step-by-step explanation:

Given :

Vertices of triangle ACB: A(-4,4), C(-1,3), B(-4,0)

Vertices of triangle YZX: Y(8,8), Z(6,2), X(0,8)

Calculation :

After the clockwise [tex]90^0[/tex] rotation.  

Rule for this transformation:  

[tex](x,y) \rightarrow (y,-x)[/tex]

After the transformation vertices of triangle ACB becomes

A'(4,4); C'(3,1); B'(0,4)  

Second transformation is a dilation with a scale factor of 2 from the origin.

Rule for this transformation:

[tex](x,y) \rightarrow (2x,2y)[/tex]

After the transformation vertices of triangle A'C'B' becomes

A"(8,8); C"(6,2); B"(0,8)  

By comparing the two triangles A"C"B" and YZX, we can see that coordinates of A" and Y, C" and Z, B" and X are same.  

Rotation is a rigid transformation, because both lengths and angles were preserved.   But dilation is not a rigid transformation because lengths are not preserved but angles are preserved.

Therefore,

[tex]\rm \angle B\cong \angle X[/tex]

[tex]\rm \angle A\cong \angle Y[/tex]

[tex]\rm \angle C\cong \angle Z[/tex]

Therefore, only one statement is true and that is,

[tex]\rm \angle A\cong \angle Y[/tex]

For more information, refer the link given below

https://brainly.com/question/24580745?referrer=searchResults

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