What are the coordinate points of A'(1,9) if A undergoes a rotation of:
90° clockwise =
270° clockwise =
To find the coordinate points of A' after a rotation of 90° clockwise, we can use the following rotation matrix:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]
Since we are rotating A by 90° clockwise, θ = -90°.
Using the rotation matrix, we can calculate the new coordinates as follows:
[x', y'] = [ cos(-90°) -sin(-90°) ] * [x, y]
[ sin(-90°) cos(-90°) ]
= [ 0 1 ] * [1, 9]
[-1 0 ]
= [1*0 + 9*-1, 1*1 + 9*0]
= [0, 1]
Therefore, the coordinate points of A' after a rotation of 90° clockwise is A'(0, 1).
Similarly, to find the coordinate points of A' after a rotation of 270° clockwise, we can use the same rotation matrix, but this time with θ = -270°.
Using the rotation matrix, we can calculate the new coordinates as follows:
[x', y'] = [ cos(-270°) -sin(-270°) ] * [x, y]
[ sin(-270°) cos(-270°) ]
= [ 0 -1 ] * [1, 9]
[ 1 0 ]
= [1*0 + 9*1, 1*-1 + 9*0]
= [9, -1]
Therefore, the coordinate points of A' after a rotation of 270° clockwise is A'(9, -1).