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EXAMPLE 2

EXAMPLE 2. Write a translation rule and verify congruence. Write a rule for the translation of ABC to A ′ B ′ C ′. Then verify that the transformation is an isometry. SOLUTION.

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EXAMPLE 2

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  1. EXAMPLE 2 Write a translation rule and verify congruence Write a rule for the translation ofABCto A′B′C′.Then verify that the transformation is an isometry.

  2. SOLUTION Use the SAS Congruence Postulate. Notice that CB =C′B′ = 3, and AC = A′C′ = 2. The slopes of CB and C′B′ are 0, and the slopes of CA and C′A′ are undefined, so the sides are perpendicular. Therefore, C and C′ are congruent right angles. So, ABCA′B′C′. The translation is an isometry. EXAMPLE 2 Write a translation rule and verify congruence To go from A to A′, move 4 units left and 1 unit up. So, a rule for the translation is (x, y) →(x –4, y + 1).

  3. 3. In Example 2, write a rule to translate A′B′C′ back to ABC. ′ To go from A to A, move 4 units right and 1 unit down. So, a rule for the translation is (x, y) →(x +4, y – 1). for Example 2 GUIDED PRACTICE SOLUTION

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