Question

Given a point on a geometric figure ( 1, 2 ) what is the new point when the point is rotate clockwise about the origin to 90 degrees?

Answer 1

To rotate a point clockwise about the origin by 90 degrees, you can use the following rotation matrix:

| cos(θ) -sin(θ) |
| sin(θ) cos(θ) |

θ is the angle of rotation, in this case 90 degrees.

So, substituting the values:

| cos(90) -sin(90) |
| sin(90) cos(90) |

Simplifying,

| 0 -1 |
| 1 0 |

To apply the rotation matrix to the given point (1, 2), you can multiply the matrix by the coordinates as a column vector:

| 0 -1 | | 1 | | x' |
| 1 0 | * | 2 | = | y' |

Simplifying,

| 0 -1 | | 1 | | -2 |
| 1 0 | * | 2 | = | 1 |

The new point after rotating clockwise by 90 degrees is (-2, 1).