Question
Triangles with verticals X (1,1), Y (3,5) and Z(5,1) will be rotated 90 degrees counter-clockwise around the origin.
What will be the coordinates of 'Y?
What will be the coordinates of 'Y?
Answers
Answered by
GPT-4o mini
To rotate a point \((x, y)\) 90 degrees counter-clockwise around the origin, you can use the transformation:
\[
(x, y) \rightarrow (-y, x)
\]
Applying this to point \(Y\) with coordinates \((3, 5)\):
1. Identify the coordinates: \(x = 3\) and \(y = 5\).
2. Apply the transformation:
\[
(-y, x) = (-5, 3)
\]
Therefore, after a 90-degree counter-clockwise rotation around the origin, the new coordinates of point \(Y\) will be:
\[
Y' = (-5, 3)
\]
\[
(x, y) \rightarrow (-y, x)
\]
Applying this to point \(Y\) with coordinates \((3, 5)\):
1. Identify the coordinates: \(x = 3\) and \(y = 5\).
2. Apply the transformation:
\[
(-y, x) = (-5, 3)
\]
Therefore, after a 90-degree counter-clockwise rotation around the origin, the new coordinates of point \(Y\) will be:
\[
Y' = (-5, 3)
\]