Question

Triangle ABC is rotated to create the image A'B'C'.

Which rule describes the transformation?

Answer 1

A rotation of 180° about the origin

Explanation:

To not the rule of rotation, you need to do the following:

1. Join A with A' and B with B'.

2. The point where the 2 lines meet is the center of rotation. Call this point X.

3. To know the angle of rotation, measure angle AXA' = BXB' = CXC'. This angle is 180°

Since the angle is a straight line, it does not matter whether it is clockwise or anticlockwise.

So the rule is "a rotation of 180° about the origin".

Answer 2

If you combine points A and A', B and B', C and C', you can see that all three lines are intersected at origin. This means that center of rotation is origin.

Now, in order to obtain point A' from point A, you have to rotate point A clockwise (or anti-clockwise) 180° about the origin; in order to obtain point B' from point B, you have to rotate point B clockwise (or anti-clockwise) 180° about the origin; in order to obtain point C' from point C, you have to rotate point C clockwise (or anti-clockwise) 180° about the origin.

That's why given rule rule describes the rotation by 180° clockwise (or anti-clockwise) about the origin.