Use the image to answer the question.

Question

Translate the figure VWXYZ
3 units to the left. Which of the following would be a vertex in the translated figure? Select all that apply.

(2 points)
Responses

(−1,3)
open paren negative 1 comma 3 close paren

(3,1)
open paren 3 comma 1 close paren

(4,−5)
open paren 4 comma negative 5 close paren

(1,1)
open paren 1 comma 1 close paren

(2,6)
open paren 2 comma 6 close paren

(−1,−2)

Answer 1

To translate the figure VWXYZ 3 units to the left, we need to subtract 3 from the x-coordinate of each vertex.

Let’s denote the original coordinates of the vertices as \((x, y)\). After translation, the new coordinates will be \((x - 3, y)\).

Now let's apply this translation to each response option:

1. \((−1, 3)\):

   • New coordinates: \((-1 - 3, 3) = (-4, 3)\)

2. \((3, 1)\):

   • New coordinates: \((3 - 3, 1) = (0, 1)\)

3. \((4, −5)\):

   • New coordinates: \((4 - 3, -5) = (1, -5)\)

4. \((1, 1)\):

   • New coordinates: \((1 - 3, 1) = (-2, 1)\)

5. \((2, 6)\):

   • New coordinates: \((2 - 3, 6) = (-1, 6)\)

6. \((−1, −2)\):

   • New coordinates: \((-1 - 3, -2) = (-4, -2)\)

Since we don't know the original vertices of VWXYZ, we can only determine which of the new coordinates could potentially match one of the vertices after translation. The translated vertices are:

• \((-4, 3)\)
• \((0, 1)\)
• \((1, -5)\)
• \((-2, 1)\)
• \((-1, 6)\)
• \((-4, -2)\)

Thus, from the given options, if we consider potential overlap, the translated coordinates do not match the original responses since we don’t have the original vertices to check against.

Hence, based on these calculations, none of the provided coordinates are confirmed results of the translation without knowing the original locations of VWXYZ.