think and discuss

Step 2 Apply the rule to find the vertices of the image. A(-1 + 3, 1 - 4) = A(2, -3) B(-3 + 3, 3 - 4) = B(0, -1) C(-4 + 3, 0 - 4) = C(-1, -4)

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Step 3 Plot the points. Then finish drawing the image by using a straightedge to connect the vertices.

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3. Find the coordinates for the image of JKLM after the translation (x, y) → (x - 2, y + 4). Draw the image.

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EXAMPLE

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Art History Application y

The pattern shown is similar to a pattern on a wall of the Alhambra. Write a rule for the translation of square 1 to square 2.

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Step 1 Choose 2 points Choose a point A on the preimage and a corresponding point A on the image. A has coordinates (3, 1), and A has coordinates (1, 3).

1 A x 3

Step 2 Translate To translate A to A, 2 units are subtracted from the x-coordinate and 2 units are added to the y-coordinate. Therefore, the translation rule is (x, y) → (x - 2, y + 2). 4. Use the diagram to write a rule for the translation of square 1 to square 3.

THINK AND DISCUSS 1. Explain how to recognize a reflection when given a figure and its image. 2. GET ORGANIZED Copy and complete the graphic organizer. In each box, sketch an example of each transformation. /À>˜ÃvœÀ“>̈œ˜Ã ,iviV̈œ˜

52

Chapter 1 Foundations for Geometry

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