EXAMPLE 1 Translate a figure in the coordinate plane

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Presentation transcript:

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.

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)

GUIDED PRACTICE for Example 1 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 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

GUIDED PRACTICE for Example 1 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) y R S T ′ x R(2, 2) → R′(3, 4) S(5, 2) → S′(6, 4) T(3, 5) → T′(4, 7)

GUIDED PRACTICE for Example 1 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. SOLUTION To find the coordinates of the endpoints of the subtract 4 from x-coordinate and add preimage 7 to y-coordinate. (x, y) → (x – 4, y + 7) P'( 3, 4) → P(– 7, 11) – Q'(2, 1) → Q(– 2, 8)