Final answer:
Using the distance formula, we can calculate these distances and find the area of the triangle which is 108 square units.
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 1/2 * base * height.
In this case, the base is the distance between points A and C, and the height is the distance between point B and the line formed by points A and C. We can find these distances using the distance formula.
Distance between A and C: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((9 - 0)^2 + (0 - 0)^2) = 9 units
Distance between B and line AC: h
= abs(Ax * (Cy - Ay) + Cx * (Ay - By) + Bx * (Ay - Cy)) / sqrt((Cx - Ax)^2 + (Cy - Ay)^2)
= abs(0 * (0 - 8) + 9 * (8 - 0) + 3 * (0 - 0)) / sqrt((9 - 0)^2 + (0 - 0)^2)
= 24 units
Using these values, we can calculate the area of the triangle: A = 1/2 * base * height
= 1/2 * 9 * 24
= 108 square units.