To rotate a point 270° clockwise, we need to determine the new coordinates of the point after the rotation.
Let's first establish the origin at the center of the geometric figure. Then, we can use the following rotation matrix:
[x'] [cosθ -sinθ] [x]
[y'] = [sinθ cosθ] [y]
In this case, the angle of rotation is 270°, or θ = 270°.
Substituting the values into the rotation matrix and applying it to the point (9, 5), we get:
[x'] [cos270° -sin270°] [9]
[y'] = [sin270° cos270°] [5]
Since cos270° = 0 and sin270° = -1, they can be substituted:
[x'] [0 -(-1)] [9]
[y'] = [(-1) 0] [5]
Simplifying:
[x'] [0 1] [9]
[y'] = [-1 0] [5]
Calculating the matrix multiplication:
[x'] = (0 * 9) + (1 * 5) = 5
[y'] = (-1 * 9) + (0 * 5) = -9
Therefore, the new point after rotating (9, 5) 270° clockwise is (-9, 5).
Rotate the point (9, 5) on a geometric figure 270° clockwise what is the new point?
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