Given a point on a line segment (−4, −6), what is the new point when the point is rotated clockwise about the origin 90 degrees?
To find the new point when rotating a point about the origin, we can use the rotation matrix:
[ cosθ -sinθ ]
[ sinθ cosθ ]
In this case, since we are rotating the point 90 degrees clockwise, θ = -90 degrees or -π/2 radians.
Plugging in the values, we get:
[ cos(-π/2) -sin(-π/2) ]
[ sin(-π/2) cos(-π/2) ]
Simplifying the trigonometric functions:
[ 0 1 ]
[ -1 0 ]
Multiplying the matrix by the point (-4, -6):
[ 0 1 ] [ -4 ] = [ 1 ]
[ -1 0 ] [ -6 ] [ -6 ]
Therefore, when the point (-4, -6) is rotated clockwise about the origin 90 degrees, the new point is (1, -6).