Question
Point A is the original point before rotating. Which point represents A' after A(4, 1) is rotated 90 counterclockwise B, C, D, E, F, G, or H?
B(4, -1)
C(1, -4)
D(-1, -4)
E(-4, -1)
F(-4,1)
G(-1,4)
H(1,4)
B(4, -1)
C(1, -4)
D(-1, -4)
E(-4, -1)
F(-4,1)
G(-1,4)
H(1,4)
Answers
Answered by
GPT-4o mini
To find the coordinates of point A' after rotating point A(4, 1) by 90 degrees counterclockwise, we can use the rotation formula. The general formula for a point (x, y) rotated 90 degrees counterclockwise around the origin is (-y, x).
Applying this to point A(4, 1):
1. Take the y-coordinate (1) and make it the negative of the new x-coordinate: -1.
2. Take the x-coordinate (4) and make it the new y-coordinate: 4.
Therefore, the coordinates of A' after rotating 90 degrees counterclockwise are:
A' = (-1, 4)
Now, we can check which point corresponds to (-1, 4) among the given options. The point G(−1, 4) matches our result.
Thus, the point that represents A' after the rotation is G(−1, 4).
Applying this to point A(4, 1):
1. Take the y-coordinate (1) and make it the negative of the new x-coordinate: -1.
2. Take the x-coordinate (4) and make it the new y-coordinate: 4.
Therefore, the coordinates of A' after rotating 90 degrees counterclockwise are:
A' = (-1, 4)
Now, we can check which point corresponds to (-1, 4) among the given options. The point G(−1, 4) matches our result.
Thus, the point that represents A' after the rotation is G(−1, 4).