Question

A landscape architect represents a flower bed by a polygon with vertices (1,0), (4,0), and (1,2). She decides to move the flower bed to a new location by translating it along the vector [-4, -3]. Where is the flower bed's final position?

Answer 1

The flower bed, originally with vertices at (1,0), (4,0), and (1,2), is translated along the vector [-4, -3] to its final position with vertices at (-3, -3), (0, -3), and (-3, -1).

Step-by-step explanation:

When a landscape architect decides to move a flower bed following a translation vector, each vertex of the polygon (in this case, the flower bed) is moved according to the translation vector. Given the initial vertices of the flower bed at (1,0), (4,0), and (1,2), and the translation vector [-4, -3], we simply add the translation vector to each vertex to find the new location:

Therefore, the final position of the flower bed's vertices are (-3, -3), (0, -3), and (-3, -1).