Rotate a point on a line at (-4, 6) 180 degrees counterclockwise. What is the resulting point

Answer 1

To rotate a point 180 degrees counterclockwise, you can use the following transformation matrix:

[ cos(α) -sin(α) ]
[ sin(α) cos(α) ]

Since we want to rotate the point (-4, 6) by 180 degrees counterclockwise, α = 180 degrees.

Therefore, the transformation matrix becomes:

[ cos(180) -sin(180) ]
[ sin(180) cos(180) ]

Simplifying the matrix:

[ -1 0 ]
[ 0 -1 ]

Now, we can apply this transformation matrix to the original point (-4, 6):

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

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