Reflections or Flips.

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Reflections or Flips

Objectives Draw reflected images Across x-axis Across y-axis
Across line y = x

Equal Distance from Reflection Line
Reflections y x Across the x-axis Multiply y coordinate by -1 y x Across the y-axis Multiply x coordinate by -1 A A’ A B B’ B C C’ C B’ KEY: Equal Distance from Reflection Line C’ A’ y x Across the line y = x Interchange x and y coordinates B A B’ C C’ A’

Common reflections in the coordinate plane
x-axis y-axis y = x Pre-image to image (a, b)  (a, -b) (a, b)  (-a, b) (a, b)  (b, a) Find coordinates Multiply y coordinate by -1 Multiply x coordinate by -1 Interchange x and y coordinates 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

Draw the reflected image of quadrilateral WXYZ in line p.
Step 1 Draw segments perpendicular to line p from each point W, X, Y, and Z. 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. 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'. Example 1-1a

Draw the reflected image of quadrilateral ABCD in line n.

COORDINATE GEOMETRY Quadrilateral 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. D' A(1, 1)  A' (1, –1) C' B(3, 2)  B' (3, –2) C(4, –1)  C' (4, 1) A' B' 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). Example 1-2a

COORDINATE GEOMETRY Quadrilateral 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. B' A(1, 1)  A' (–1, 1) A' B(3, 2)  B' (–3, 2) C(4, –1)  C' (–4, –1) C' D(2, –3)  D' (–2, –3) D' Answer: The x-coordinates are opposite, but the y-coordinates stay the same. That is, (a, b)  (–a, b). Example 1-3a

COORDINATE GEOMETRY Suppose 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'. C' A(1, 2)  A'(2, 1) B' B(3, 5)  B'(5, 3) D' C(4, –3)  C'(–3, 4) A' 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). Example 1-5a

Summary & Homework Summary: Homework:
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 ; , 28-30, 35-36, 44-47 Reflection x-axis y-axis origin y = x Pre-image to image (a, b)  (a, -b) (a, b)  (-a, b) (a, b)  (-a, -b) (a, b)  (b, a) Find coordinates Multiply y coordinate by -1 Multiply x coordinate by -1 Multiply both coordinates by -1 Interchange x and y coordinates