To determine the kind of translation that maps quadrilateral ABCD to quadrilateral EHGF, we need to identify the relationship between the corresponding vertices of the two quadrilaterals.
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Identify the vertices: Identify the coordinates of the vertices of quadrilateral ABCD (let's say A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), D(x₄, y₄)) and the coordinates of the vertices of quadrilateral EHGF (E(x₅, y₅), H(x₆, y₆), G(x₇, y₇), F(x₈, y₈)).
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Calculate the translation vector: The translation can be described by a vector (T_x, T_y) that indicates how much each point moves in the x and y directions. This vector can be found by examining the transformation of any corresponding points. For example, if point A moves to point E, then the translation vector is:
\[ T_x = x_5 - x_1 \] \[ T_y = y_5 - y_1 \]
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Check consistency: Ensure that this translation vector is consistent for the other pairs of corresponding points:
- B to H
- C to G
- D to F
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Conclusion: If the same translation vector applies to all corresponding pairs of points, then we have confirmed that a simple translation has been used to map ABCD to EHGF.
If you have specific coordinates, you could use those to compute the exact translation. In general, if a direct correspondence of points corroborates this calculation, it indicates a translation transformation with the defined vector.
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