Question
Rotate the point (−4, −6) on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses
To rotate a point 90 degrees counterclockwise on a geometric figure, you can use the rotation matrix formula:
| cosθ -sinθ |
| sinθ cosθ |
where θ is the angle of rotation.
In this case, since we want to rotate the point (-4, -6) 90 degrees counterclockwise, we can set θ = -90 degrees.
Using the rotation matrix formula:
| cos(-90) -sin(-90) |
| sin(-90) cos(-90) |
= | 0 1 |
|-1 0 |
Now we can multiply the rotation matrix by the original point (-4, -6):
| 0 1 | | -4 | | (0*-4) + (1*-6) | | -6 |
|-1 0 | | -6 | = | (-1*-4) + (0*-6) | = | 4 |
Therefore, the new point after rotating (-4, -6) 90 degrees counterclockwise is (6, 4).