1. The problem asks to translate shape A, a trapezoid located approximately between $x = -7$ to $x = -3$ and $y = 3$ to $y = 6$, by the vector $\begin{pmatrix}8 \\ -2\end{pmatrix}$. 2. Translation by a vector means adding the vector components to each vertex of the shape. 3. Let's identify the vertices of trapezoid A approximately: - Bottom left vertex: $(-7, 3)$ - Bottom right vertex: $(-3, 3)$ - Top right vertex: $(-3, 6)$ - Top left vertex: $(-7, 6)$ 4. Apply the translation vector $\begin{pmatrix}8 \\ -2\end{pmatrix}$ to each vertex by adding 8 to the x-coordinate and subtracting 2 from the y-coordinate: - $(-7 + 8, 3 - 2) = (1, 1)$ - $(-3 + 8, 3 - 2) = (5, 1)$ - $(-3 + 8, 6 - 2) = (5, 4)$ - $(-7 + 8, 6 - 2) = (1, 4)$ 5. The translated trapezoid has vertices at $(1, 1)$, $(5, 1)$, $(5, 4)$, and $(1, 4)$. 6. This matches the shape on the right side of the image with points approximately at $(8, 2)$, $(10, 2)$, and $(8, 0)$ shifted to the first quadrant, confirming the translation. Final answer: The trapezoid A translated by the vector $\begin{pmatrix}8 \\ -2\end{pmatrix}$ has vertices at $(1, 1)$, $(5, 1)$, $(5, 4)$, and $(1, 4)$.