How to find value of rotation angle
Answers
Step-by-step explanation:
A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point.
The fixed point is called the centre of rotation.
The amount of rotation is called the angle of rotation and it is measured in degrees.
You can use a protractor to measure the specified angle counterclockwise.
Consider the figure below.
Here, ΔA'B'O is obtained by rotating ΔABO by 180° about the origin. Observe that both AOA' and BOB' are straight lines.
So, m∠AOA'=180°=m∠BOB'.
Example:
How many degrees has the ΔXYZ been rotated counterclockwise to obtain the ΔX'Y'Z'?
A. 90°B. 180°C. 270°D. 360°
Identify the corresponding vertices of the rotation.
X(−6,2)→X'(2,6)Y(−2,4)→Y'(4,2)Z(−4,5)→Z'(5,4)
The point of rotation is the origin, draw lines joining one of the points, say X and it's an image to the origin.
You can see that the lines form an angle of 270°, in the counterclockwise direction.
Therefore, ΔX'Y'Z' is obtained by rotating ΔXYZ counterclockwise by 270° about the origin.
So, the correct choice is C.
Also note that the relation between the corresponding vertices is (x,y)→(−y,x) which shows a counterclockwise rotation of 270° about the origin.