Question

Translate triangle A by vector (-3,1) to give triangle B. Then rotate your triangle B 180 degrees around the origin to give triangle C. Describe fully the single transformation that maps triangle A onto triangle C.

Answer 1

To map triangle A onto triangle C, perform a translation by (-3,1) and then rotate 180 degrees around the origin.

Step-by-step explanation:

To map triangle A onto triangle C, we need to perform two transformations: translation and rotation.

1. To translate triangle A by the vector (-3,1), we shift each vertex of triangle A to a new position by moving it -3 units horizontally and 1 unit vertically. The new vertices form triangle B.
2. To rotate triangle B 180 degrees around the origin, we flip each vertex of triangle B to a new position by reflecting it across the x-axis. The new vertices form triangle C.

Therefore, the single transformation that maps triangle A onto triangle C is a translation by vector (-3,1) followed by a rotation of 180 degrees around the origin.