What are the coordinates of point 𝐵′ B'B

Question

′
if 𝐵 (−2, 3) B\ \left(-2,\ 3\right)B (−2, 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.

𝐵′= B'=B
′
=

Answer 1

To rotate a point (x, y) around the origin by an angle θ in a clockwise direction, you can use the following formula:

\[ (x', y') = (y, -x) \]

For Point B(-2, 3), we need to rotate it 270° clockwise. However, a 270° clockwise rotation is equivalent to a 90° counterclockwise rotation, which we can use the same formula.

Using the formula for a 90° counterclockwise rotation:

1. Start with the point B(-2, 3).
2. Apply the formula: \[ (x', y') = (y, -x) = (3, -(-2)) = (3, 2) \]

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

\[ B' = (3, -2) \]

So the final answer is:

\[ B' = (3, -2) \]