Point A is translated by the vector $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$. We need to circle the new position of point A after the translation.

1. Problem Description

Point A is translated by the vector $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$. We need to circle the new position of point A after the translation.

2. Solution Steps

Let's denote the initial coordinates of point A as $(x, y)$. From the image, we can approximate the coordinates of point A to be $(1, 2)$.

The translation vector is $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$. This means we need to add 2 to the x-coordinate and 4 to the y-coordinate of point A.

The new coordinates $(x', y')$ of point A after the translation are given by:

$x' = x + 2$

$y' = y + 4$

Substituting $x = 1$ and $y = 2$ into the above equations, we get:

$x' = 1 + 2 = 3$

$y' = 2 + 4 = 6$

So, the new coordinates of point A are $(3, 6)$. By examining the graph, the point at $(3,6)$ corresponds to the point in the upper-right corner.

3. Final Answer

The new position of point A after the translation is the point located at (3, 6) on the grid, which is the point in the upper-right corner.