Question

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0, 0).

Answer 1

The rotation of the quadrilateral ABCD about the origin (0, 0), to get the quadrilateral A'B'C'D' is 30°

How can the angle of rotation be found?

The coordinates of the vertices of rectangle ABCD are;

A(-2, 3), B(-3, 4), C(-6, 2), D(-4, 0)

The coordinates of the corresponding point D' is (-3.5, -2)

The angle formed at the vertex O of triangle ODD' is found as follows;

OD = OD' = 4

The correct x-coordinate of point D' is therefore -√(16 - 4) = -2•√3

The length of DD' is therefore;

DD' = √((-4 - (-2•√3))² + (0 - (-2))²) = 2•√6 - 2•√2

Using cosine rule, we have;

32 - 16•√3 = 2×4² - 2×4²×cos(A)

cos(A) = (2×4² - (32 - 16•√3))/(2×4²) = √3/2

• A = arccos(√3/2) ≈ 30°

Therefore;

• The angle of rotation is 30°

Learn more about rotation transformation here:

brainly.com/question/24263250

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