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Warm-Up If Brandon was standing at point (-2, 2) and moved 5 spaces to the right and

Warm-Up If Brandon was standing at point (-2, 2) and moved 5 spaces to the right and 6 spaces down, in which quadrant would he be located?. TRANSFORMATIONS in the Coordinate Plane.

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Warm-Up If Brandon was standing at point (-2, 2) and moved 5 spaces to the right and

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  1. Warm-Up If Brandon was standing at point (-2, 2) and moved 5 spaces to the right and 6 spaces down, in which quadrant would he be located?

  2. TRANSFORMATIONSin the Coordinate Plane Objective: As a result in learning, students should be able to perform translations and describe the effects on the coordinates. CCES: 8>G.8, 8.G.2, 8.G.3, MP1, MP2, MP3, MP 6, MP7

  3. What do you remember about geometric transformations? More specifically, translations?

  4. Volunteersfor Activity?

  5. A TRANSFORMATION is when a figure or point is moved to a new position in a coordinate plane. This move may include a change in size as well as position. A RIGID TRANSFORMATION when the size and shape remain the same but the figure moves into a new position.

  6. There are four types of movement (TRANSFORMATIONS): • TRANSLATION……(Slide) • ROTATION…….…..(Turn) • REFLECTION……..(Flip) • DILATION…(Enlarges or Reduces)

  7. Today we will work with TRANSLATIONS Stop and do Translation Activity Once ACTIVITY is complete, we will come back to the powerpoint and add to our notes.

  8. TRANSLATION is a movement of a figure that involves a slide in the x or y direction on a coordinate plane. More than one move may take place. Here is what a translation may look like. Notice that the direction the triangle is pointing did not change.

  9. You have discovered that there are two methods to perform a “TRANSLATION”. Each will give you the new “prime points”.

  10. METHOD 1: From each point, conduct the move requested one point at a time and then draw in your new image. Example: Plot points A(-2, 3), B(-6, 3), and C(-2, 7). Translate the figure 8 units right and 5 units down. C STEP 1:Plot original points STEP 2:From each original point move 8 units right and 5 units down. STEP 3:Connect the new points. This is your image and the points are the “prime” points. B A A(-2,3) A’(6, -2) B(-6,3) B’(2, -2) C(-2,7) C’(6, 2) STEP 4: Now list the location of the new points as your “primes”.

  11. METHOD 2: A right/left move will affect the x coordinate and an up/down move will affect the y coordinate. You can just do the arithmetic to each part of the ordered pair (coordinates). Example: Plot points A(-2, 3), B(-6, 3), and C(-2, 7). If the figure is translated 8 units right and 5 units down, name the prime points. The 8 units right will add 8 to the x number in the coordinate set and the 5 units down will subtract 5 from the y x y A(-2,3) -2 + 8 = 6 and 3 – 5 = -2 A’(6, -2) B(-6,3) -6 + 8 = 2 and 3 – 5 = -2 B’(2, -2) C(-2,7) -2 + 8 = 6 and 7 – 5 = 2 C’(6, 2)

  12. Summary • Describe the difference between the pre-image and image. • Are the pre-image and image congruent? Similar? How do you know? • If you were only given the coordinates of a figure, how could you determine if it was the pre-image or image? • Which coordinate is changed when you translate a figure to the right or left? Up or down?

  13. TRANSFORMATIONSin the Coordinate Plane

  14. Review: A TRANSFORMATION is . . . . . . . when a figure or point is moved to a new position in a coordinate plane. This move may include a change in size as well as position. A RIGID TRANSFORMATION is . . . . . . when the size and shape remain the same but the figure moves into a new position.

  15. What are four types of TRANSFORMATIONS? • TRANSLATION……(Slide) • ROTATION…….…..(Turn) • REFLECTION……..(Flip) • DILATION…(Enlarges or Reduces)

  16. Today we will work with ROTATIONS Stop and do Rotation Activity Once ACTIVITY is complete, we will come back to the powerpoint and add to our notes.

  17. ROTATION is a movement of a figure that involves rotating in 90 degree increments around the origin. The new prime points will be in the quadrant that is the given number of degrees clockwise or counterclockwise from the original figure.

  18. The easiest way to find the prime points for a given rotation is to apply the rules below: 90 degree CLOCKWISE: Coordinates flip and the NEW y changes signs 90 degree COUNTER-CLOCKWISE: Coordinates flip and the NEW x changes signs. 180 degree turn: Coordinates keep the same order and EACH one changes to opposite sign of original.

  19. ROTATION EXAMPLE 1: 90 degree clockwise move: A(5, 6) A’(6, -5) B(-3, 8) B’(8, 3) C(9, -7) C’(-7, -9) D(-4, -2) D’(-2, 4) ROTATION EXAMPLE 2: 90 degree counter-clockwise move: A(5, 6) A’(-6, 5) B(-3, 8) B’(-8, -3) C(9, -7) C’(7, 9) D(-4, -2) D’(2, -4) ROTATION EXAMPLE 3: 180 degree turn: A(5, 6) A’(-5, -6) B(-3, 8) B’(3, -8) C(9, -7) C’(-9, 7) D(-4, -2) D’(4, 2)

  20. Summary • If a pre-image begins in quadrant 2 and is rotated 90 degrees clockwise, which quadrant contains the image? • An image is located in the 4th quadrant. If the pre-image is located in the 3rd, how was it rotated? • A point, (-2, 7) is rotated 180 degrees. What are its new coordinates?

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