transformations (Reflections)

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Presentation transcript:

transformations (Reflections) Today’s Lesson: What: transformations (Reflections) Why: . . . so I can both identify and perform reflections on the coordinate plane. How: . . . by taking accurate notes, participating, and completing homework.

A reflection over the “x” axis changes which variable?

A reflection over the “y” axis changes which variable?

Short introduction to reflections . . .

flip y axis What is a Reflection?? A reflection is a ____________ . We will reflect on the coordinate plane over both the x axis and the ___________________________ . A AI flip y axis

(Repeat above process for all points on figure) How do we perform a reflection?? Identify the line of reflection, or the line that the figure will ____________ over. Choose a point on the original figure (pre-image), and count the number of grid lines that lie between the point and the line of __________________ . Then, count out the ___________ number of grid lines on the OTHER side of the line of reflection. This is where the new point will be (the “prime” point). (Repeat above process for all points on figure) flip reflection SAME Example

Reflect the figure over the “x” axis: Perform the following reflections: Reflect the figure over the “x” axis: Matching points MUST be the same distance from the line of reflection! A B C D CI DI BI AI Point A: (-3, 6) Point AI : _______ (-3,-6) Hmmm, what is interesting about above points?

Hmmm, notice that only the “x” value changed! Perform the following reflections: Reflect the figure over the “y” axis: How can you tell that the below transformation is a reflection and NOT a translation?? AI BI A B C D DI CI Point A: (7, 5) Point AI : _______ (-7, 5) Hmmm, notice that only the “x” value changed!

Reflect the figure over the “x” axis: Perform the following reflections: Reflect the figure over the “x” axis: BI AI CI A B C Point A: (-1, -8) Point AI : _______ (-1, 8) This time, only the “y” value changed! Why?? Hint: “Right or left changes x! Up or down changes y!”

Reflect the figure over the “y” axis: Perform the following reflections: Reflect the figure over the “y” axis: A B C CI AI BI Point A: (-1, -7) Point AI : _______ (1, -7) By now, we can see that a RIGHT/LEFT flip changes X to its opposite; while an UP/DOWN flip changes ____ to its opposite!! This always works! y

Wrap-it-up/summary: It changes the “y” variable to its opposite. A reflection over the “x” axis changes which variable? . . . over the “y” axis? It changes the “y” variable to its opposite. It changes the “x” variable to its opposite.

Finish homework worksheet (handed out in class).

END OF LESSON