Question

Points $A(3,5)$ and $B(7,10)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.

Answer 1

10.25π units²

Explanation:

Area of the circle = πd²/4

Given the end point of the diameter of a circle as A(3,5) and B(7,10), the distance between the two points will be the diameter of the circle.

Using the formula

|AB| = √(y2-y1)²+(x2-x1)²

x1 = 3, y1 = 5, x2 = 7, y2 = 10

|AB| = √(10-5)²+(7-3)²

|AB| = √5²+4²

|AB| = √25+16

|AB| = √41

Diameter of the circle = √41 units

Area of the circle = π(√41)²/4

Area of the circle = 41π/4

Area of the circle = 10.25π units²