Mathematics, 22.10.2019 23:00 chanahvanya

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

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Answer from: beauty2624

Only one Statement is True : $\rm \angle A\cong \angle Y$

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 90^0 rotation.

Rule for this transformation:

$(x,y) \rightarrow (y,-x)$

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:

$(x,y) \rightarrow (2x,2y)$

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,

$\rm \angle B\cong \angle X$

$\rm \angle A\cong \angle Y$

$\rm \angle C\cong \angle Z$

Therefore, only one statement is true and that is,

$\rm \angle A\cong \angle Y$

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Answer from: ashiteru123

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 ∠ 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 from: Quest

Use basic math on google

Answer from: Quest

step-by-step explanation:

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