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Korvikt [17]
3 years ago
6

What points do I graph the image of the rotation on?

Mathematics
1 answer:
leva [86]3 years ago
6 0

Answer:

see attached

Step-by-step explanation:

No doubt you have seen that the tranformation that rotates a figure 270° CCW is the same as the one that rotates a figure 90° CW:

(x, y) ⇒ (y, -x)

This means the coordinate A(-3, 1) rotates to the position A'(1, 3). In this figure, that happens to coincide with point B.

When I drew this figure and the center of rotation O(0, 0), I was a little surprised to see the four points form a square. That makes it unsurprising that the point A gets rotated to point B by the desired transformation. (When you rotate a square 90° (or 270°) about one corner, an adjacent vertex (corner) will line up with the other adjacent vertex (corner).

_____

If you need to get a feel for rotations, so you can do this better in the future, it might be helpful to trace the figure (and the axes) onto a piece of tissue paper or tracing paper, then rotate it the necessary amount and see where the figure ends up.

This exercise may be easier with a print of the figure, but you can do it on a computer screen, too. (A touch screen makes it more difficult.)

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When you have 3 choices for each of 6 spins, the number of possible "words" is
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A) The probability of a word containing two of each of the letters is 90/729 = 10/81


The number of permutations of 6 things from two groups of different sizes is
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B) The number of ways there can be at least 2 "a"s and no "b"s is
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_____
These numbers were verified by listing all possibilities and actually counting the ones that met your requirements.
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