The three basic types of rigid transformations are rotation, reflection and translation transformation
The correct options are;
Quadrilateral ABCD is reflected over the x-axis → (2, 4)
Quadrilateral ABCD translated 2 units right and 1 unit down → (4, -5)
Quadrilateral ABCD dilated about the origin by a scale factor of 3 → (6, -12)
Quadrilateral ABCD rotated 180° clockwise about the origin → (-2, 4)
The reasons the above matches are correct are as follows:
The given coordinates of the preimage are A(2, -4)
The image of (x, y) following a reflection over the x-axis is (x, -y)
Therefore
- A(2, -4) in Quadrilateral ABCD is reflected over the x-axis → A'(2, 4)
The image of (x, y) following a translation of 2 units right and 1 unit down → (x + 2, y - 1)
Therefore;
- A(2, -4) in Quadrilateral ABCD translated 2 units right and 1 unit down → A'(4, -5)
The image of (x, y) following a dilation about the origin by a scale factor of 3 is (3×x, 3×y)
Therefore;
- A(2, -4) in Quadrilateral ABCD dilated about the origin by a scale factor of 3 → A'(6, -12)
The image of the point (x, y) rotated 180° clockwise about the origin is (-x, -y)
Therefore;
- A(2, -4) in Quadrilateral ABCD rotated 180° clockwise about the origin → A'(-2, 4)
Learn more about rigid transformations here:
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