The rotation of the quadrilateral ABCD about the origin (0, 0), to get the quadrilateral A'B'C'D' is 30°
<h3>How can the angle of rotation be found?</h3>
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 <em>D'</em><em> </em>is (-3.5, -2)
The angle formed at the vertex <em>O </em>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
Therefore;
- The angle of rotation is 30°
Learn more about rotation transformation here:
brainly.com/question/24263250
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