We are given the coordinates of point B as $(2, 7)$ and the vector $\vec{AB} = \begin{pmatrix} -4 \\ 6 \end{pmatrix}$. We need to find the coordinates of point A.

1. Problem Description

We are given the coordinates of point B as $(2, 7)$ and the vector $\vec{AB} = \begin{pmatrix} -4 \\ 6 \end{pmatrix}$. We need to find the coordinates of point A.

2. Solution Steps

Let the coordinates of point A be $(x, y)$.

We know that $\vec{AB} = \begin{pmatrix} 2-x \\ 7-y \end{pmatrix}$.

We are given that $\vec{AB} = \begin{pmatrix} -4 \\ 6 \end{pmatrix}$.

Therefore, we have the following equations:

$2 - x = -4$

$7 - y = 6$

Solving for $x$:

$2 - x = -4$

$x = 2 + 4$

$x = 6$

Solving for $y$:

$7 - y = 6$

$y = 7 - 6$

$y = 1$

Therefore, the coordinates of point A are $(6, 1)$.

3. Final Answer

The coordinates of point A are $(6, 1)$.