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Answer :
A translation moves every point of a figure by the same fixed vector. In this problem, each point [tex]\((x,y)\)[/tex] is shifted to [tex]\((x-4,\,y-3)\)[/tex]. This means the translation vector is
[tex]$$
(-4, -3).
$$[/tex]
A translation is a type of rigid motion (an isometry). Rigid motions preserve distances, so they maintain the shape and size of a figure. Consequently, the following properties of quadrilateral [tex]\(WXYZ\)[/tex] remain unchanged after the transformation:
1. The side lengths are preserved.
2. The perimeter is the same.
3. The area is also the same.
Thus, the correct statement is that the area of the quadrilateral remains unchanged. In other words,
[tex]$$
\text{Area of } WXYZ = \text{Area of its image after the translation.}
$$[/tex]
Therefore, the true statement is:
[tex]$$
\text{"The area of quadrilateral } WXYZ \text{ is equal to the area of quadrilateral } WXYZ."
$$[/tex]
[tex]$$
(-4, -3).
$$[/tex]
A translation is a type of rigid motion (an isometry). Rigid motions preserve distances, so they maintain the shape and size of a figure. Consequently, the following properties of quadrilateral [tex]\(WXYZ\)[/tex] remain unchanged after the transformation:
1. The side lengths are preserved.
2. The perimeter is the same.
3. The area is also the same.
Thus, the correct statement is that the area of the quadrilateral remains unchanged. In other words,
[tex]$$
\text{Area of } WXYZ = \text{Area of its image after the translation.}
$$[/tex]
Therefore, the true statement is:
[tex]$$
\text{"The area of quadrilateral } WXYZ \text{ is equal to the area of quadrilateral } WXYZ."
$$[/tex]
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