Question

rotate a point on a line at (-4,6) 180 degrees counterclockwise. whats the resulting point?

Answer 1

To rotate a point 180 degrees counterclockwise on a plane, we need to multiply the coordinates of the point by a rotation matrix:

R = [cos(θ) -sin(θ)]
[sin(θ) cos(θ)]

Since we want to rotate the point 180 degrees counterclockwise, θ (theta) would be 180 degrees.

When we substitute θ = 180 degrees into the rotation matrix, we get:

R = [-1 0]
[ 0 -1]

Multiplying the rotation matrix by the coordinates of the point (-4, 6) gives us:

Resulting point = R * [-4, 6]

= [(-1)(-4) + (0)(6), (0)(-4) + (-1)(6)]

= [4, -6]

Therefore, the resulting point after rotating the point (-4, 6) 180 degrees counterclockwise is (4, -6).