Point A is the original point before rotating. Which point represents A' after A (4, 1) is rotated 90 degrees counterclockwise: B, C, D, E, F, G, or H?
To find the new coordinates of point A' after rotating point A (4, 1) 90 degrees counterclockwise, we can use the rotation matrix for a counterclockwise rotation of 90 degrees:
| cos(θ) -sin(θ) |
| sin(θ) cos(θ) |
In this case, θ = 90 degrees, so the rotation matrix becomes:
| cos(90) -sin(90) |
| sin(90) cos(90) |
Simplifying this, we get:
| 0 -1 |
| 1 0 |
Now, we can multiply the rotation matrix by the coordinates of point A (4, 1):
| 0 -1 | * | 4 |
| 1 0 | | 1 |
This gives us the new coordinates after rotating point A:
| 0*(-1) + (-1)*(1) |
| 1*4 + 0*1 |
Simplifying, we get:
| -1 |
| 4 |
Therefore, the new coordinates of point A' after rotating A (4, 1) 90 degrees counterclockwise are (-1, 4).
Now, looking at the possible points B, C, D, E, F, G, and H, we can see that none of them match the coordinates (-1, 4). Thus, none of these points represent A'.