What are the coordinates of point 𝐶′ C'C

Question

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if 𝐶 (10, 3) C\ \left(10,\ 3\right)C (10, 3) is rotated 270°270\degree270° clockwise around the origin. Click for Help Video.

Your answer must be listed as a coordinate so use parenthesis.

Answer 1

To rotate a point \( C(x, y) \) 270° clockwise around the origin, we can use the following transformation rule:

For a rotation of 270° clockwise, the new coordinates \( (x', y') \) can be calculated as: \[ (x', y') = (y, -x) \]

Given \( C(10, 3) \), we can apply the transformation:

1. \( x = 10 \)
2. \( y = 3 \)

Now we will substitute these values into the transformation:

\[ x' = 3 \] \[ y' = -10 \]

Thus, the coordinates of point \( C' \) after the rotation are:

\[ C'(3, -10) \]

So, the answer is \( (3, -10) \).