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.

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.

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Piper 7 days 2021-10-08T01:59:33+00:00 1 Answer 0

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    2021-10-08T02:01:28+00:00

    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

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