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.

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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.

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). 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, ABC A′B′C′. The translation is an isometry. SOLUTION

GUIDED PRACTICE for Example 2 In Example 2, write a rule to translate A ′ B ′ C ′ back to ABC. 3. SOLUTION 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). ′