Question

If P(3, 2) and Q(7, 10) are the endpoints of the diameter of a circle, what is the area of the circle in square units? ​ a. b. 20π c. 80π d.

Answer 1

Answer:

The correct answer is option (b).

Therefore the area of the circle is   $=20 \pi$  square units

Step-by-step explanation:

Given that , P(3,2) and Q(7,10) are the endpoint of the diameter of a circle.

To find out the length of diameter we use the distance formula.

If (x₁,y₁) and (x₂,y₂) are point.

Then the distance between them is = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here x₁=3,y₁=2,x₂ = 7,y₂=10.

The length of the diameter is = $\sqrt{(7-3)^2+(10-2)^2}$

                                                  $=\sqrt{80}$ units.

Radius of a circle $=\frac{Dameter}{2}$

Therefore the the radius of the circle is $=\frac{\sqrt{80}}{2}$ units $=\frac{2\sqrt{20} }{2}$  units $=\sqrt{20}$ units

The area of a circle = $\pi r^2$

Therefore the area of the circle is $=\pi (\sqrt{20})^2$

                                                        $=20 \pi$  square units