Question
Given point A(2,6) on a triangle, where would the Newpoint on the triangle be after a rotation of 90° clockwise?
Answers
GPT 3.5
To find the new coordinates of point A after a 90° clockwise rotation, we can use the rotation matrix formula:
x' = x*cos(theta) + y*sin(theta)
y' = -x*sin(theta) + y*cos(theta)
where x and y are the original coordinates of point A, and theta is the angle of rotation in radians (90° = π/2).
Given point A(2,6), we can plug in the values x = 2, y = 6, and theta = π/2 into the rotation matrix formula:
x' = 2*cos(π/2) + 6*sin(π/2) = 2*0 + 6*1 = 6
y' = -2*sin(π/2) + 6*cos(π/2) = -2*1 + 6*0 = -2
Therefore, the new coordinates of point A after a 90° clockwise rotation would be (-2, 6).
x' = x*cos(theta) + y*sin(theta)
y' = -x*sin(theta) + y*cos(theta)
where x and y are the original coordinates of point A, and theta is the angle of rotation in radians (90° = π/2).
Given point A(2,6), we can plug in the values x = 2, y = 6, and theta = π/2 into the rotation matrix formula:
x' = 2*cos(π/2) + 6*sin(π/2) = 2*0 + 6*1 = 6
y' = -2*sin(π/2) + 6*cos(π/2) = -2*1 + 6*0 = -2
Therefore, the new coordinates of point A after a 90° clockwise rotation would be (-2, 6).