Given a point on a line segment -4 -6 what is the new point when the point is rotated clockwise about the origin 90°
To rotate a point (-4, -6) 90° clockwise about the origin, we can use the rotation matrix formula:
[x', y'] = [cosθ -sinθ; sinθ cosθ] * [x, y]
Since the angle of rotation is 90°, we have:
[x', y'] = [cos90° -sin90°; sin90° cos90°] * [-4, -6]
Evaluating the trigonometric functions, we get:
[x', y'] = [0 -(-1); 1 0] * [-4, -6]
= [0 1; 1 0] * [-4, -6]
= [0*-4 + 1*-6, 1*-4 + 0*-6]
= [6, -4]
Therefore, when the point (-4, -6) is rotated clockwise about the origin 90°, the new point is (6, -4).