Question

demonstrating the properties of rotation if a line segment with endpoint zero 3 and zero and 7 is rotated 90 clockwise what is the endpoint of the rotation segment

Answer 1

To find the endpoint of the line segment after rotating it 90 degrees clockwise, we can use the rotation matrix formula:

[x', y'] = [cos(θ), sin(θ); -sin(θ), cos(θ)] * [x, y]

Given that the initial endpoint is (0, 7) and we want to rotate it 90 degrees clockwise, we have:

θ = -90 degrees = -π/2 radians

Plugging the values into the formula:

[x', y'] = [cos(-π/2), sin(-π/2); -sin(-π/2), cos(-π/2)] * [0, 7]

Using the values of the cosine and sine of -π/2:
cos(-π/2) = 0
sin(-π/2) = -1

Now calculating the matrix multiplication:

[x', y'] = [0, -1; 1, 0] * [0, 7]

This gives us:
x' = 0*0 + (-1)*7 = -7
y' = 1*0 + 0*7 = 0

Therefore, the endpoint of the rotated line segment is (-7, 0).