given a point (-7, 4) On a genetic figure, what is the new point after rotating the figure 90° clockwise?
To find the new point after rotating a figure 90° clockwise, we need to use the rotation matrix:
[R] = cos(θ) -sin(θ)
sin(θ) cos(θ)
Where θ represents the angle of rotation.
In this case, we have a 90° clockwise rotation:
θ = -90° = -π/2 radians
Using the rotation matrix, we can calculate the new coordinates:
[x'] = cos(-π/2) -sin(-π/2) [x]
[y'] = sin(-π/2) cos(-π/2) [y]
Simplifying the expressions:
[x'] = 0*(-7) + (-1)*(4) = 0 - 4 = -4
[y'] = 1*(-7) + 0*(4) = -7 + 0 = -7
Therefore, the new point after rotating (-7, 4) 90° clockwise is (-4, -7).