The point Z

Question

(
–
6
,
6
)
is rotated 270
°
counterclockwise around the origin. What are the coordinates of the resulting point, Z
'
?
Z
'
,

Answer 1

To rotate the point \( Z(-6, 6) \) counterclockwise by \( 270^\circ \) around the origin, we can use the following transformation rules for rotation:

1. A \( 90^\circ \) counterclockwise rotation transforms a point \( (x, y) \) to \( (-y, x) \).
2. A \( 180^\circ \) counterclockwise rotation transforms a point \( (x, y) \) to \( (-x, -y) \).
3. A \( 270^\circ \) counterclockwise rotation (which is equivalent to a \( 90^\circ \) clockwise rotation) transforms a point \( (x, y) \) to \( (y, -x) \).

Since we are looking for a \( 270^\circ \) counterclockwise rotation of point \( Z(-6, 6) \):

1. Start with the coordinates of \( Z \): \( (-6, 6) \).

2. Apply the conversion for a \( 270^\circ \) counterclockwise rotation:

   \[ Z' = (y, -x) = (6, -(-6)) = (6, 6) \]

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

\[ Z' = (6, -6) \]