If area of triangle is 35 sq units with vertices `(2, - 6), (5, 4) a n d (k , 4)`. Then k is
(A) 12 (B) `-2` (C) ` 12 , 2` (D) `12 , 2`

Explanation

To find the value of \( k \) given that the area of the triangle with vertices \( (2, -6) \), \( (5, 4) \), and \( (k, 4) \) is 35 square units, we can use the formula for the area of a triangle based on its vertices.

### Step-by-Step Solution:

1. **Area Formula**: The area \( A \) of a triangle with vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) can be calculated using the determinant:
\[
A = \frac{1}{2} \left| \begin{vmatrix}
x_1 & y_1 & 1 \\
...