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Translations in the Coordinate Plane

Students will be able to predict the results of translations and draw translations on the coordinate plane. . Translations in the Coordinate Plane. Review. Introduction Video to Translations. http://www.youtube.com/watch?v=XdjH_EWhCZ0. Vocabulary. Transformation- maps one figure onto another

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Translations in the Coordinate Plane

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  1. Students will be able to predict the results of translations and draw translations on the coordinate plane. Translations in the Coordinate Plane

  2. Review

  3. Introduction Video to Translations • http://www.youtube.com/watch?v=XdjH_EWhCZ0

  4. Vocabulary • Transformation-maps one figure onto another • Translation-the motion of moving a figure without turning it • Congruent Figures- same size and shape, and the corresponding sides and angles have equal measures

  5. Translations in the Coordinate Plane

  6. Draw a Translation

  7. Check Your Progress

  8. Find Coordinates of a Translation

  9. Check Your Progress Triangle TUV has vertices T(6,-3), U(-2,0), and V(-1,2). Find the vertices of triangle T’U’V’ after a translation of 3 units right and 4 units down. Then graph the figure an its translated image.

  10. Students will be able to predict the results of a reflection and graph reflections on a coordinate plane. Reflections in the Coordinate Plane

  11. Symmetry in Reflections • Scientists have determined that the human eye uses symmetry to see. It is possible to understand what you are looking at even if you do not see all of it.

  12. A, B, C, D… • List all of the capital letters of the alphabet that look exactly the same when folded across a vertical line.

  13. Vocabulary Line Symmetry: Figures that match exactly when folded in half have line symmetry. Line Symmetry: Each fold line is called a line of symmetry.

  14. Practice and Apply • Determine whether each figure has line symmetry. If so, copy the figure and draw all lines of symmetry.

  15. Practice and Apply • Copy each figure. Draw the resulting figure when each figure is lipped over line.

  16. Reflections in Nature • Does the size and shape remain the same on either side of the line of symmetry? • What do you notice about the distance from the points to the line of symmetry?

  17. Vocabulary • Reflection- A mirror imaged produced by flipping a figure over a line • Line of Reflection- The line in which an image is flipped to form a reflection • Image- the location or position of a figure after a transformation

  18. How to draw a reflection • Count the units between a point and the line of reflection. • For each point (vertex), plot a point an equal distance away from the line of reflection on the reflected side • Connect the vertices to form the reflected image.

  19. Example • Reflect the image over the y-axis

  20. You Try • Reflect the figure using the x axis as a line of reflection. X (4, -4) Y (-2,-3) Z (2, -1) What do you notice about the old coordinates and the new coordinates? Is there a pattern?

  21. Discover the rule for the y-axis • Graph triangle FGH with vertices F (1,-1) G (5, -3), H (2, -4). Graph the image of triangle FGH after the reflection over the y axis. • Compare the new coordinates to the old coordinates to find your rule.

  22. Reflecting Figures over axes X-Axis The x values remain the same, the y value changes sign Y-Axis The y values remain the same, the x value changes the sign.

  23. Exit Pass • Graph the figure with the given vertices. Then graph the image of the figure after a reflection over the x-axis. Then graph the image after it has been translated up 2 units and right 3. **Be sure to write the coordinates of the image’s vertices.

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