What is the measurement of C if the image is rotated 350° clockwise

Question

C(2,2) A(2,5) B(5,2)

Answer 1

To find the measurement of C after rotating the image 350° clockwise, we need to apply the rotation formula using the coordinates of C,A, and B.

First, let's find the rotation matrix that represents a clockwise rotation of 350°. The rotation matrix for a clockwise rotation by angle θ is given by:

[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]

In our case, θ = 350°, so the rotation matrix becomes:

[ cos(350°) -sin(350°) ]
[ sin(350°) cos(350°) ]

Next, let's express the coordinates of points A(2,5) and B(5,2) as column vectors:

A = [2, 5]
B = [5, 2]

We will multiply the rotation matrix by the column vectors representing the points A and B to obtain the rotated coordinates:

C' = [ cos(350°) -sin(350°) ] * [2, 5] = [ cos(350°)*2 - sin(350°)*5, sin(350°)*2 + cos(350°)*5 ]
[ sin(350°) cos(350°) ] [ sin(350°)*2 + cos(350°)*5, cos(350°)*2 - sin(350°)*5 ]

Finally, let's substitute the values of sin(350°) and cos(350°) using the unit circle or trigonometric identities. We get:

sin(350°) = sin(360° - 10°) = -sin(10°)
cos(350°) = cos(360° - 10°) = cos(10°)

Now we can substitute the values into the coordinates of C':

C' = [ cos(10°)*2 - (-sin(10°))*5, -sin(10°)*2 + cos(10°)*5 ]
[ -sin(10°)*2 + cos(10°)*5, cos(10°)*2 - (-sin(10°))*5 ]

C' = [ 2cos(10°) + 5sin(10°), -2sin(10°) + 5cos(10°) ]
[ -2sin(10°) + 5cos(10°), 2cos(10°) + 5sin(10°) ]

Therefore, the coordinates of C after rotating the image 350° clockwise are approximately:

C' = [ 2cos(10°) + 5sin(10°), -2sin(10°) + 5cos(10°) ]

Now, you can substitute the value of cos(10°) and sin(10°) using a calculator to find the approximate coordinates of C'.