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Understanding Vector Transformations in Geometry

Learn how to translate figures and use vectors to transform shapes accurately in geometry, preserving length and angles. Practice finding preimage coordinates and translating vertices.

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Understanding Vector Transformations in Geometry

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  1. Chapter 9 Section 9. 1 – Translate Figures and Use Vectors.

  2. Key Vocabulary. • Image: Transformation that moves or changes a figure in some way to produce a new figure. • Preimage: The original figure. • Isometry: Transformation that preserves length and angle measure (congruent transformation). • Vector: a quantity that has both magnitude and direction • Translation: A translation is an isometry.

  3. Solution:

  4. Solution:

  5. The image of (x, y) → (x + 4, y – 7) is P′Q′ with endpoints P′(–3, 4) and Q′(2, 1). Find the coordinates of the endpoints of the preimage. – P'( 3, 4) → P(– 7, 11) Q'(2, 1) → Q(– 2, 8) GUIDED PRACTICE SOLUTION To find the coordinates of the endpoints of the preimage subtract 4 from the X- coordinate and add 7 to the Y- coordinate. (x, y) → (x – 4, y + 7)

  6. GUIDED PRACTICE The vertices of ∆LMN are L(2, 2), M(5, 3), and N(9, 1). Translate ∆LMN using the vector –2, 6 . SOLUTION Find the translation of each vertex by subtracting 2 from its x-coordinate and adding 6 to its y-coordinate. (x, y) → (x – 2, y + 6) L(2, 2) → L′(0, 8) M(5, 3) → M′(3, 9) N(9, 1) → N′(7, 7)

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