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In quadrilateral ABCD, A = (0, 0), B = (3, 2), C = (4, −2), and D = (3, −3). Describe the image of ABCD under the translation T<−4, 2> by dragging and dropping the vertices of ABCD to the corresponding vertices of T<−4, 2>(ABCD).

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Answer:

In quadrilateral ABCD, A = (0, 0), B = (3, 2), C = (4, −2), and D = (3, −3). Describe the image of ABCD under the translation T<−4, 2> by dragging and dropping the vertices of ABCD to the corresponding vertices of T<−4, 2>(ABCD).

Step-by-step explanation:

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The image of ABCD is formed by points [tex]A'(x,y) = (-4, 2)[/tex], [tex]B'(x,y) = (-1, 4)[/tex], [tex]C'(x,y) = (0, 0)[/tex] and [tex]D'(x,y) = (-1, -1)[/tex].

Vectorially speaking, a translation is defined by the following formula:

[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)

Where:

  • [tex]P(x,y)[/tex] - Original point.
  • [tex]T(x,y)[/tex] - Translation vector.
  • [tex]P'(x,y)[/tex] - Resulting point.

If we know that [tex]A(x,y) = (0,0)[/tex], [tex]B(x,y) = (3, 2)[/tex], [tex]C(x,y) = (4, -2)[/tex], [tex]D(x,y) = (3, -3)[/tex] and [tex]T(x,y) = (-4,2)[/tex], then the resulting points of the rectangle are:

[tex]A'(x,y) = (0, 0) + (-4, 2)[/tex]

[tex]A'(x,y) = (-4, 2)[/tex]

[tex]B'(x,y) = (3, 2) + (-4,2)[/tex]

[tex]B'(x,y) = (-1, 4)[/tex]

[tex]C'(x,y) = (4,-2) + (-4, 2)[/tex]

[tex]C'(x,y) = (0, 0)[/tex]

[tex]D'(x,y) = (3, -3) + (-4, 2)[/tex]

[tex]D'(x,y) = (-1, -1)[/tex]

The image of ABCD is formed by points [tex]A'(x,y) = (-4, 2)[/tex], [tex]B'(x,y) = (-1, 4)[/tex], [tex]C'(x,y) = (0, 0)[/tex] and [tex]D'(x,y) = (-1, -1)[/tex].

We kindly invite to check this question on translations: https://brainly.com/question/12463306

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