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The point (x,y) is rotated 180 degrees counterclockwise about the origin. Write a rule to determine the coordinate of the image (x, y). Explain how you found the rule.

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sqdancefan

Answer:

  (x, y) ⇒ (-x, -y)

Step-by-step explanation:

There are a couple of ways you can go at this.

1) Rotation by 180° in either direction is the same as reflection across the origin. That reflection is identical to reflection across both the x- and y-axes, in either order, so negates both coordinates. The transformation rule is ...

  (x, y) ⇒ (-x, -y)

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2) The rule for a general rotation by angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

For α = 180°, sin(α) = 0 and cos(α) = -1. This makes the rule for rotation by 180° be ...

  (x, y) ⇒ (-x, -y)

myawengerd
If a point (x , y) is rotated 180 degrees counter clockwise around the origin, you take the opposites of that point so it now becomes (-x , -y). I hope that helps!!

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