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EXAMPLE 1

EXAMPLE 1. Translate a figure in the coordinate plane. Graph quadrilateral ABCD with vertices A (–1, 2) , B (–1, 5) , C (4, 6), and D (4, 2) . Find the image of each vertex after the translation ( x , y ) →( x + 3, y – 1) . Then graph the image using prime notation. SOLUTION.

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EXAMPLE 1

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  1. EXAMPLE 1 Translate a figure in the coordinate plane Graph quadrilateral ABCD with vertices A(–1, 2), B(–1, 5), C(4, 6), and D(4, 2). Find the image of each vertex after the translation (x, y) →(x + 3, y – 1).Then graph the image using prime notation. SOLUTION First, draw ABCD. Find the translation of each vertex by adding 3 to its x-coordinate and subtracting 1 from its y-coordinate. Then graph the image.

  2. EXAMPLE 1 Translate a figure in the coordinate plane Graph quadrilateral ABCD with vertices A(–1, 2), B(–1, 5), C(4, 6), and D(4, 2). Find the image of each vertex after the translation (x, y) →(x + 3, y – 1).Then graph the image using prime notation. (x, y) → (x + 3, y – 1) A(–1, 2) → A′(2, 1) B(–1, 5) → B′(2, 4) C(4, 6) → C′(7, 5) D(4, 2) → D′(7, 1)

  3. First, draw . Find the translation of each vertex by adding 1 to its x-coordinate and adding 2 to its y-coordinate. Then graph the image. RST for Example 1 GUIDED PRACTICE 1. Draw RST with vertices R(2, 2), S(5, 2), and T(3, 5). Find the image of each vertex after the translation (x, y) → (x + 1, y + 2). Graph the image using prime notation. SOLUTION

  4. y T R S x ′ ′ ′ T R S for Example 1 GUIDED PRACTICE Graph triangle RST with vertices R(2, 2), S(5, 2), T(3, 5). Find the image of each vertex after the translation (x, y) →(x + 1, y + 2).Then graph the image using prime notation. (x, y) → (x + 1, y + 2) R(2, 2) → R′(3, 4) S(5, 2) → S′(6, 4) T(3, 5) → T′(4, 7)

  5. 2. 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) for Example 1 GUIDED PRACTICE SOLUTION

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