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Reflections or Flips

Reflections or Flips. Objectives. Draw reflected images Across x-axis Across y-axis Across line y = x. Across the y-axis. Across the x-axis. y. y. y. Multiply x coordinate by -1. Multiply y coordinate by -1. x. x. x. Across the line y = x. Interchange x and y coordinates.

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Reflections or Flips

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  1. Reflections orFlips

  2. Objectives • Draw reflected images • Across x-axis • Across y-axis • Across line y = x

  3. Across the y-axis Across the x-axis y y y Multiply x coordinate by -1 Multiply y coordinate by -1 x x x Across the line y = x Interchange x and y coordinates Reflections A A A’ B B’ B C C’ C KEY: EqualDistancefromReflectionLine B’ C’ A’ B A B’ C A’ C’

  4. Common reflections in the coordinate plane A line of symmetry is like a line of reflection. The line of symmetry in a figure is a line where the figure could be folded in half so that the two halves match exactly

  5. Step 2 Locate W', X', Y', and Z' so that line p is the perpendicular bisector of Points W', X', Y', and Z' are the respective images of W, X, Y, and Z. Example 1-1a Draw the reflected image of quadrilateral WXYZin line p. Step 1 Draw segments perpendicular to line p from each point W, X, Y, and Z. Answer: Since points W', X', Y', and Z' are the images of points W, X, Y, and Z under reflection in line p, then quadrilateral W'X'Y'Z' is the reflection of quadrilateral WXYZ in line p. Step 3 Connect vertices W', X', Y', and Z'.

  6. Example 1-1b Draw the reflected image of quadrilateral ABCD in line n. Answer:

  7. Example 1-2a D' C' A' B' COORDINATE GEOMETRYQuadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the x-axis. Compare the coordinates of each vertex with the coordinates of its image. Use the vertical grid lines to find the corresponding point for each vertex so that the x-axis is equidistant from each vertex and its image. A(1, 1) A' (1, –1) B(3, 2) B' (3, –2) C(4, –1) C' (4, 1) D(2, –3) D' (2, 3) Answer: The x-coordinates stay the same, but the y-coordinates are opposite. That is, (a, b)  (a, –b).

  8. B' A' C' D' Example 1-3a COORDINATE GEOMETRYQuadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the y-axis. Compare the coordinates of each vertex with the coordinates of its image. Use the horizontal grid lines to find the corresponding point for each vertex so that the y-axis is equidistant from each vertex and its image. A(1, 1) A' (–1, 1) B(3, 2) B' (–3, 2) C(4, –1) C' (–4, –1) D(2, –3) D' (–2, –3) Answer: The x-coordinates are opposite, but the y-coordinates stay the same. That is, (a, b)  (–a, b).

  9. C' B' D' A' Example 1-5a COORDINATE GEOMETRYSuppose quadrilateral ABCD with A(1, 2), B(3, 5), C(4, –3), and D(2, –5) is reflected in the line y = x. Graph ABCD and its image under reflection in the line y = x. Compare the coordinates of each vertex with the coordinates of its image. The slope of y = x is 1. AA’ is perpendicular to y = x so its slope is –1. From A to the line y = x move down ½ unit and right ½ unit. From the line y = x move down ½ unit, right ½ unit to A'. A(1, 2)  A'(2, 1) B(3, 5)  B'(5, 3) C(4, –3)  C'(–3, 4) D(2, –5)  D'(–5, 2) Plot the reflected vertices and connect to form the image A'B'C'D'. Answer: The x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate. That is, (a, b)  (b, a).

  10. Summary & Homework • Summary: • Line of Symmetry – a line across which the figure could be folded in half • Point of Symmetry – even numbered regular figures only for us • Homework: • pg 467-469; 15-17, 28-30, 35-36, 44-47

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