Final answer:
To find the area of the circle in terms of u, we can substitute the radius into the formula A = πr². The area of the circle is 193π/4, so the answer is option d) πu.
Step-by-step explanation:
The area of a circle can be found using the formula A = πr², where A is the area and r is the radius of the circle. In this case, we need to find the radius of the circle first. The distance between the endpoints of the diameter is equal to the diameter of the circle. Using the distance formula, we find that the diameter of the circle is √[(x₂ - x₁)² + (y₂ - y₁)²]. Substituting the coordinates of the endpoints, we have √[(5 - (-7))² + (-3 - 4)²] = √(144 + 49) = √193. Since the radius is half the diameter, the radius of the circle is √193/2.
To find the area of the circle in terms of u, we substitute √193/2 for r in the formula A = πr². This gives us A = π(√193/2)² = π(193/4) = 193π/4.
Therefore, the answer is option d) πu.