Question

If A(3,4) and B(10,4) are the end points of a diameter of circle "O", what is the area of the circle O

Answer 1

Answer:

$\large\boxed{\dfrac{49\pi}{4}}$

Step-by-step explanation:

The formula of an area of a circle:

$A=\pi r^2$

r - radius

We have the endpoints of a diameter of a circle.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the given points A(3, 4) and B(10, 4):

$d=\sqrt{(10-3)^2+(4-4)^2}=\sqrt{7^2+0^2}=\sqrt{7^2}=7$

Therefore we have the length of the diameter: d = 7

We know: d = 2r. Therefore

$r=\dfrac{7}{2}$

Substitute to the formula of an area:

$A=\pi\left(\dfrac{7}{2}\right)^2=\dfrac{49\pi}{4}$

There is no such answer in the answers to choose.

Apparently you have some error in the coordinates of the endpoints.