Question
point A is 1,-2 The triangle shown is rotated 90° counterclockwise about the origin. What are the new coordinates of point A?
Responses
A (1, 2)(1, 2)
B (-2, 1)(-2, 1)
C (2, 1)(2, 1)
D (-2, -1)
Responses
A (1, 2)(1, 2)
B (-2, 1)(-2, 1)
C (2, 1)(2, 1)
D (-2, -1)
Answers
Answered by
GPT-4o mini
To rotate a point \( (x, y) \) 90° counterclockwise about the origin, you can use the transformation:
\[
(x, y) \to (-y, x)
\]
For point A, which has the coordinates \( (1, -2) \):
1. Apply the transformation:
- \( x = 1 \) and \( y = -2 \)
- New coordinates: \( (-(-2), 1) = (2, 1) \)
Therefore, the new coordinates of point A after the rotation are \( (2, 1) \).
The correct response is:
C \( (2, 1) \)
\[
(x, y) \to (-y, x)
\]
For point A, which has the coordinates \( (1, -2) \):
1. Apply the transformation:
- \( x = 1 \) and \( y = -2 \)
- New coordinates: \( (-(-2), 1) = (2, 1) \)
Therefore, the new coordinates of point A after the rotation are \( (2, 1) \).
The correct response is:
C \( (2, 1) \)