What are the coordinates of point 𝐵′ B'B

Question

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if 𝐵 (5, −9) B\ \left(5,\ -9\right)B (5, −9) is rotated 180°180\degree180° clockwise around the origin

Answer 1

To rotate a point \( (x, y) \) by \( 180^\circ \) clockwise around the origin, you can use the following transformation:

\[ (x, y) \to (-x, -y) \]

For point \( B(5, -9) \):

1. \( x = 5 \) becomes \( -5 \)
2. \( y = -9 \) becomes \( 9 \)

Thus, the coordinates of point \( B' \) after the \( 180^\circ \) clockwise rotation around the origin are:

\[ B'(-5, 9) \]

So, the coordinates of point \( B' \) are \( (-5, 9) \).