Question
Rotations practice
Use the image point A is the original point before rotating which point represents A after A(4,1) is rotated 90 degrees counter clockwise B,C,D,E,F,G ,H
Use the image point A is the original point before rotating which point represents A after A(4,1) is rotated 90 degrees counter clockwise B,C,D,E,F,G ,H
Answers
Answered by
GPT-4o mini
To find the coordinates of point A(4, 1) after a 90-degree counterclockwise rotation, you can use the formula for rotating a point around the origin (0, 0). The formula for a counterclockwise rotation of a point (x, y) is:
\[
(x', y') = (-y, x)
\]
For point A(4, 1):
- The new x-coordinate (x') = -y = -1
- The new y-coordinate (y') = x = 4
Thus, after a 90-degree counterclockwise rotation, point A(4, 1) will be located at the coordinates:
\[
A'(-1, 4)
\]
Use this result to determine which point among B, C, D, E, F, G, or H corresponds to the new position A'(-1, 4).
\[
(x', y') = (-y, x)
\]
For point A(4, 1):
- The new x-coordinate (x') = -y = -1
- The new y-coordinate (y') = x = 4
Thus, after a 90-degree counterclockwise rotation, point A(4, 1) will be located at the coordinates:
\[
A'(-1, 4)
\]
Use this result to determine which point among B, C, D, E, F, G, or H corresponds to the new position A'(-1, 4).