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 angle C after rotating the image 350° clockwise, we need to find the coordinates of the new position of point C after the rotation.

To do this, we can use the formula for rotating a point (x,y) a certain number of degrees clockwise:

x' = x*cosθ - y*sinθ
y' = x*sinθ + y*cosθ

In this case, the coordinates of point C are (2,2), and we want to rotate the image 350° clockwise.

Using the formula, we can calculate the coordinates of the new position of point C:

x' = 2*cos(350°) - 2*sin(350°)
y' = 2*sin(350°) + 2*cos(350°)

After evaluating these expressions, we get approximately:

x' ≈ 1.45
y' ≈ 0.17

Therefore, the new position of point C after rotating the image 350° clockwise is approximately (1.45, 0.17).

Now, we can find the measurement of angle C by using the coordinates of point C and the coordinates of points A and B:

Slope of line AC = (y_A - y_C) / (x_A - x_C)
Slope of line BC = (y_B - y_C) / (x_B - x_C)

Using the coordinates A(2,5), B(5,2), and C(1.45, 0.17), we can substitute these values into the slope formulas:

Slope of line AC = (5 - 0.17) / (2 - 1.45)
Slope of line BC = (2 - 0.17) / (5 - 1.45)

After evaluating these expressions, we get:

Slope of line AC ≈ 4.83
Slope of line BC ≈ 0.97

Since the slopes of line AC and line BC are not equal, we can conclude that angle C is not a right angle (90°).

Therefore, we cannot determine the measurement of angle C with the given information.