Question

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

Answer 1

The flower bed's final position after being translated by the vector [-4, -3] will have the vertices at (-3,-3), (0,-3), (0,-1), and (-3,-1).

Step-by-step explanation:

The landscape architect's flower bed represented by a polygon can be translated to a new position using the given vector. Each vertex of the flower bed will be moved according to the vector [-4, -3]. The vertices in the final position can be obtained by subtracting 4 from the x-coordinate and 3 from the y-coordinate of the original vertices.

1. Translate vertex (1,0) by vector [-4, -3] to get new vertex (-3,-3).
2. Translate vertex (4,0) by vector [-4, -3] to get new vertex (0,-3).
3. Translate vertex (4,2) by vector [-4, -3] to get new vertex (0,-1).
4. Translate vertex (1,2) by vector [-4, -3] to get new vertex (-3,-1).

Therefore, the flower bed's final position will have vertices at the following ordered pairs: (-3,-3), (0,-3), (0,-1), and (-3,-1).