Question

The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point A of the preimage. Point D′ of the image coincides with point B of the preimage.

Answer 1

The statement is true that, when a regular hexagon ABCDEF is rotated 240º counterclockwise about its centre to form hexagon A′B′C′D′E′F′, the point C′ of the image coincides with point A of the preimage and point D′ of the image coincides with point B of the preimage.

• The angle between the sides of a regular hexagon at the centre is 60º.
• So, when we rotate the hexagon taking the starting point as A, then the angle between points A and F is 60º,  and the same continues.
• So, the angle between points A and E is 60º + 60º = 120º
• Similarly, the angle between points A and D is 120º + 60º = 180º
• And, the angle between points A and C is 180º + 60º = 240º
• Implies that the pre-image of A coincides with the image of C when the angle is rotated anticlockwise.
• Similarly, considering the angle between the points B and the rest, we get, the angle between points B and A is 60º,  and the same continues.
• So, the angle between points B and F is 60º + 60º = 120º
• Similarly, the angle between points B and E is 120º + 60º = 180º
• And, the angle between points B and D is 180º + 60º = 240º
• Implies that the pre-image of B coincides with the image of D when the angle is rotated anticlockwise.

Answer 2

Answer:Point D' coincides with point F

Step-by-step explanation: