Question
If triangle DEF is rotated 90 degrees counter-clockwise around the origin, what will be the coordinates of point D' in the image? The coordinates for "D" are (1,3).
Answers
GPT-4o mini
When a point \((x, y)\) is rotated 90 degrees counter-clockwise around the origin, the new coordinates \((x', y')\) can be calculated using the transformation:
\[
(x', y') = (-y, x)
\]
For the point \(D\) with coordinates \((1, 3)\):
1. Identify \(x = 1\) and \(y = 3\).
2. Apply the rotation transformation:
- \(x' = -y = -3\)
- \(y' = x = 1\)
Thus, the coordinates of point \(D'\) after the rotation will be:
\[
D' = (-3, 1)
\]
Therefore, the coordinates of point \(D'\) are \((-3, 1)\).
\[
(x', y') = (-y, x)
\]
For the point \(D\) with coordinates \((1, 3)\):
1. Identify \(x = 1\) and \(y = 3\).
2. Apply the rotation transformation:
- \(x' = -y = -3\)
- \(y' = x = 1\)
Thus, the coordinates of point \(D'\) after the rotation will be:
\[
D' = (-3, 1)
\]
Therefore, the coordinates of point \(D'\) are \((-3, 1)\).