Final answer:
The area of triangle ABC is 24 square units. Therefore, the correct option is C.
Step-by-step explanation:
Let’s first find the length of the altitude from A to BC.
The slope of BC is (3 - (-3)) / (3 - (-3)) = 6/6 = 1.
Therefore, the slope of the line perpendicular to BC is -1.
The equation of the line BC is y = x.
The equation of the line perpendicular to BC and passing through A is y - 4 = -1(x + 4), which simplifies to y = -x.
Solving the system of equations y = x and y = -x gives us the intersection point of the two lines as (0, 0).
Therefore, the length of the altitude from A to BC is the distance between A and (0, 0), which is 4√2.
Now, we can use the formula for the area of a triangle: 1/2 * base * height.
The base is the length of BC, which is √((3 - (-3))^2 + (3 - (-3))^2) = 6√2.
The height is the length of the altitude from A to BC, which is 4√2.
Therefore, the area of ΔABC is 1/2 * 6√2 * 4√2
= 24 square units
Therefore, the correct option is C.