Question

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

Answer 1

wrong

Answer 2

To rotate a point clockwise about the origin by 90 degrees, we need to use the following transformation matrix:

| cos(θ) -sin(θ) |
R = | sin(θ) cos(θ) |

Where θ is the angle of rotation (90 degrees in this case).

Let's apply this transformation to the given point (1, 2):

| cos(90) -sin(90) | | 1 | | 0 |
R = | sin(90) cos(90) | * | 2 | = |-2 |

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

So, the new point when (1, 2) is rotated clockwise about the origin by 90 degrees is (-2, 0).

Answer 3

Apologies for the mistake. Let's correct it.

To rotate a point (x, y) clockwise about the origin by 90 degrees, we can swap the x and y coordinates and change the sign of the new x-coordinate. So, for the point (1, 2):

The new x-coordinate = -2
The new y-coordinate = 1

Therefore, the new point when (1, 2) is rotated clockwise about the origin by 90 degrees is (-2, 1).