Giving 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 about the origin by 90° clockwise, we can use the following rotation formula:
(x', y') = (x·cosθ - y·sinθ, x·sinθ + y·cosθ)
In this case, the point to be rotated is (-4, -6) and we want to rotate it by 90° clockwise, so θ = -90°.
(x', y') = (-4·cos(-90°) - (-6)·sin(-90°), -4·sin(-90°) + (-6)·cos(-90°))
Using trigonometric identities, we know that cos(-90°) = 0 and sin(-90°) = -1.
(x', y') = (-4·0 - (-6)·(-1), -4·(-1) + (-6)·0)
Simplifying,
(x', y') = (0 - 6, 4 + 0)
Therefore, the new point after rotating (-4, -6) clockwise about the origin by 90° is (6, 4).