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Transformations and the Coordinate Plane

Transformations and the Coordinate Plane. I. II. Do you remember the QUADRANTS?. (+,+). (-,+). (-,-). (+,-). Do you remember the SIGNS for each Quadrant?. III. IV. TRANSLATION (slide). Move Right = add to x Move Left = subtract from x Move Up = Add to y Move Down = Subtract from y.

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Transformations and the Coordinate Plane

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  1. Transformations and the Coordinate Plane

  2. I II Do you remember the QUADRANTS? (+,+) (-,+) (-,-) (+,-) Do you remember the SIGNS for each Quadrant? III IV

  3. TRANSLATION (slide) • Move Right = add to x • Move Left = subtract from x • Move Up = Add to y • Move Down = Subtract from y

  4. Give the (x+-,y+-) coordinate for each Translation: 1 to 3 5 to 2 1 to 2 4 to 5 4 to 3 1 to 4 1 2 (x + 2, y – 8) 5 (x – 2, y + 3) (x + 7, y) 3 4 (x, y + 7) (x – 7, y + 2) (x + 9, y – 10)

  5. What if you don’t have graph paper? Translate the following points 5 units to the left and 2 units up: (-4, 2) (0,0) (5, -2) (-3, -5) Translate 2 units down and 3 units to right: (3, -8) (-2, 3) (0, 5) (-8, -3) (-5, 2) (0, 0) (-9, 4) (6, -10) (1, 1) (3, 3)

  6. Reflection (flip) • Across the x-axis: change the sign of the y value • Across the y-axis:change the sign of the x value • Across the origin (i.e. y=x or y = -x): switch the x and y • Across any other line: points are equal distance from the reflection line. • y = # makes a horizontal line • x = # makes a vertical line.

  7. The trapezoid LMNO is reflected across the x axis. Notice how the numbers change. L (-7, 5) L’ (-7, -5) M (0,5) M’ (0,-5) N (-2,1) N’ (-2, -1) O (-5, 1) O’ (-5, -1) What if we were to reflect LMNO over the y-axis. What would the new coordinates be? L’ (7,5) M’ (0,5) N’ (2,1) O’ (5,1) What if we reflected LMNO over the ORIGIN? L’ (5,-7) M’ (5,0) N’ (1,-2) O’ (1, -5)

  8. No graph paper??? No problem!! We have triangle ABC with the following points: A: (-2,3), B: (5,4), and C: (2, -4) Reflect Triangle ABC across the y-axis……. A’ (2,3) B’ (-5,4) C’ (-2,-4 Reflect Triangle ABC across the x-axis…….. A’ (-2,-3) B’ (5,-4) C’ (2, 4) Reflect Triangle ABC across the origin…… A’ (3,-2) B’ (4,5) C’ (-4,2) http://www.waldomaths.com/Reflections1NLW.jsp

  9. Rotations (turn) Around Origin • 90° counterclockwise (aka270 ° clockwise): switch x and y, then change the sign of the new x-value • 180°: change the sign of the x-value and y-value • 90 ° clockwise (aka 270° counterclockwise) : switch x and y, then change the sign of the new y-value

  10. C Rotate Triangle ABC 90° clockwise around origin. A (2, 5)……Switch the numbers to get (5,2). Since we are going into quadrant IV, the x will be + and the y will be -. Thus our new point A’ = (5,-2) Using the same rule, what is B’ and C’ B (8,6) B’ (6, -8) C (4,9) C’ (9, -4) B A Rotate ABC 180° around origin. A (2,5)……Leave the numbers the same to get (2,5). Since we are going into quadrant III, both x and y will be -. A’’ is (-2, -5) Find points B and C using the same rule. B: (8,6) C: (4,9) B’: (-8, -6) C’: ( -4, -9)

  11. No graph paper at home????It’s OK! (-,+) (+,+) (-,-) (+,-) Rotate these around the ORIGIN!! A (3, -2) clockwise 90° B (0, 5) 180° C (-3,-7) counterclockwise 90° D (2,3) clockwise 90° E (-3, 6) 180° F (-7, -2) clockwise 90° G (5, 1) clockwise 270° (-2,-3) (0,-5) (7,-3) (3,-2) (3,-6) (-2,7) (-1,5)

  12. The Transformation Song….(tune of Happy and You Know It)http://www.youtube.com/watch?v=IvgEU25SmME • When you REFLECT across the x, you change the y. (clap clap) • When you REFLECT across the y, you change the x. (clap clap) • When the numbers switch you’ll see, it’s across the origin you’ll be. • Reflection is fun for you and me! • When you rotate 90 degrees, you switch the numbers. (stomp stomp) • When you rotate ninety degrees, you check the quadrant. (stomp stomp) • When you rotate 180 degrees, only the signs will switch you’ll see • Rotation is fun for you and me!! When you translate right or left, you move the x. (yippee) • When you translate up or down, you move the y. (yippee) • It’s the easiest one we’ve tried, all the figures do is slide • Translation is fun for you and me.

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