rotate the point (-4,-6) on a geometric figure 180 degrees counterclockwise. what is the new point?
To rotate a point 180 degrees counterclockwise, we can multiply the coordinates of the point by the matrix:
[ cos(180) -sin(180) ]
[ sin(180) cos(180) ]
where cos(180) = -1 and sin(180) = 0.
Multiplying the coordinates of the point (-4, -6) by the matrix, we get:
[ -1 0 ] [ -4 ] [ -1*(-4) + 0*(-6) ] [ 4 ]
[ 0 -1 ] * [ -6 ] = [ 0*(-4) + (-1)*(-6) ] = [ 6 ]
Therefore, the new point after rotating (-4, -6) 180 degrees counterclockwise is (4, 6).