Question

Anthony draws a quadrilateral ABCD and investigates the reflections and rotations that carry it onto itself Anthony claims that a rotation of 360 regress is the only transformation that carries onto itself. Select the transformation that can be used to show that claim is correct

a. A rotation of 90 degree clockwise about its centre
b. A reflection over diagnol AC
c. A reflection over side AD
d. A rotation of 180 degrees about one of its vertices

Answer 1

Anthony's claim can be challenged with several possible transformations such as reflections over diagonals or sides, and rotations of 90 or 180 degrees, depending on the properties of quadrilateral ABCD.

Step-by-step explanation:

The student's claim that a rotation of 360 degrees is the only transformation that carries a quadrilateral onto itself is incorrect. Several other transformations can also achieve this, depending on the specific properties of the quadrilateral ABCD. For instance:

• A reflection over diagonal AC, if ABCD is a kite or a rhombus.
• A reflection over side AD, if ABCD is a rectangle or a square.
• A rotation of 90 degrees clockwise about its centre if ABCD is a square.
• A rotation of 180 degrees about its centre if ABCD is a rectangle or a square.

To definitively challenge Anthony's claim, we would need to know the specific properties of the quadrilateral he has drawn.