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 ? (1 point)

Answer 1

The point A(4, 1) will be rotated 90° counterclockwise around the origin.

To find the new coordinates, we can use the rotation formula:

x' = x * cosθ - y * sinθ
y' = x * sinθ + y * cosθ

In this case, θ = 90°.

Plugging in the values:
x' = 4 * cos(90°) - 1 * sin(90°) = 0 - 1 = -1
y' = 4 * sin(90°) + 1 * cos(90°) = 4 + 0 = 4

Therefore, the new coordinates for A(4, 1) after a 90° counterclockwise rotation will be A'(-1, 4).

Among the given points B, C, D, E, F, G, and H, none of them matches the coordinates (-1, 4).