TRANSFORMATIONS in the Coordinate Plane

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Presentation transcript:

TRANSFORMATIONS in the Coordinate Plane

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.

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

Today we will work with REFLECTIONS

which is the (line of symmetry). REFLECTION is a movement of a figure that involves flipping the figure over the given line of reflection. The new prime points will be the same distance from the line of reflection as the original points but on the opposite side of the line of reflection which is the (line of symmetry).

EXAMPLE OF REFLECTION: Plot points A(3, 2), B(7, 2), and C(7, 6) then reflect the figure over the x axis and name your new prime points. A’ ( 3 , -2 ) B’ ( 7 , -2 ) C’ ( 7 , -6 ) Notice that each point is the same distance above and below the x axis The line that you are using to “reflect” over is called the LINE OF SYMMETRY

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

A(-2,3) A’(2, 3) B(-6,3) B’(6, 3) C(-2,7) C’(2, 7) 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). Reflect the figure over the y axis. C C’ STEP 1: Plot original points STEP 2: From each original count the number of units from the y-axis and move the same distance on the opposite side of the y-axis STEP 3: Connect the new points. This is your image and the points are the “prime” points. B A B’ A’ STEP 4: Now list the location of the new points as your “primes”. A(-2,3) A’(2, 3) B(-6,3) B’(6, 3) C(-2,7) C’(2, 7)

y-coordinate if reflecting over the x-axis. METHOD 2: A reflection will only affect the x-coordinate if reflecting over the y-axis and . . . will only affect the y-coordinate if reflecting over the x-axis.

A (-2, 3) reflected over the x-axis A’ (-2, -3) Example 1: Plot points A(-2, 3), B(-6, 3), and C(-2, 7) and reflect over the x-axis: A (-2, 3) reflected over the x-axis A’ (-2, -3) B (-6, 3) reflected over the x-axis B’ (-6, -3) C (-2, 7) reflected over the x-axis C’ (-2, -7) *NOTE that the x value stayed the same and the y value became its own opposite. Example 2: Plot points A(-2, 3), B(-6, 3), and C(-2, 7) and reflect over the y-axis: A (-2, 3) reflected over the y-axis A’ (2, 3) B (-6, 3) reflected over the y-axis B’ (6, 3) C (-2, 7) reflected over the y-axis C’ (2, 7) *NOTE that the y value stayed the same and the x value became its own opposite.

Quick Questions When a pre-image is reflected over the x-axis, what happens to the coordinates? Over the y-axis? Are the pre-image and image congruent? Similar? How do you know? Use points A(-3, -5), B(-1, -2), and C(-1, -6) What would the coordinates of the image be if the figure was flipped over the x-axis? The y-axis?