Question

Given a point on a geometric figure (1, 2) , what is the new point when the point is rotated clockwise about the origin 90 degrees?(1 point)
give the right awnser please

Answer 1

To rotate a point (x, y) clockwise about the origin by 90 degrees, we can use the following rotation matrix:

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

For a clockwise rotation of 90 degrees, θ = -90 degrees. Converting this to radians gives θ = -π/2.

Applying the rotation matrix to the point (1, 2):

|x'| |cos(-π/2) -sin(-π/2)| |1|
| | = | | * | |
|y'| |sin(-π/2) cos(-π/2) | |2|

Simplifying the matrix multiplication:

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

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

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

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

Therefore, the new point after rotating (1, 2) clockwise by 90 degrees is (2, 1).