Question

A segment has endpoints X(−10,0) and Y(−2,6) . Consider its image after a 180° (counterclockwise) rotation about the origin. Select the coordinates of Y′

A. Y'(2,-6)
B. Y'(6,-2)
C.Y'(-6,2)
D. Y'(-2, -6)

Answer 1

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Answer 2

To find the coordinates of the point \( Y' \) after a \( 180^\circ \) counterclockwise rotation about the origin, you can use the following rule:

For any point \( (x, y) \), after a \( 180^\circ \) rotation about the origin, the new coordinates will be \( (-x, -y) \).

Starting with the coordinates of point \( Y(-2, 6) \):
- The \( x \) coordinate is \( -2 \), so after rotation it will be \( -(-2) = 2 \).
- The \( y \) coordinate is \( 6 \), so after rotation it will be \( -6 \).

Thus, the coordinates of \( Y' \) after the rotation will be \( (2, -6) \).

So, the correct answer is:
**A. \( Y'(2, -6) \)**.

Answer 3

Let's double-check the rotation of point \( Y(-2, 6) \) by \( 180^\circ \) counterclockwise about the origin.

For a \( 180^\circ \) rotation, the transformation is given by:

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

Applying this to point \( Y(-2, 6) \):

1. The \( x \)-coordinate is \( -2 \):
- After rotation: \( -(-2) = 2 \)

2. The \( y \)-coordinate is \( 6 \):
- After rotation: \( -6 \)

So the coordinates of \( Y' \) after the rotation would be \( (2, -6) \).

Therefore, the correct answer indeed is:
**A. \( Y'(2, -6) \)**.

If you have any further questions or concerns, feel free to ask!