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Problem

Points A(-1, -2)and B(3, 2) 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.

 Apr 16, 2019
 #1
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+1

 

Points A(-1, -2)and B(3, 2) 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.

 

Think of the horizontal distance on the plane  (from –1 to 3 = 4 units) as the base of a right triangle,

and think of the vertical distance on the plane (from –2 to 2 = 4 units) as the height of that right triangle.

 

Use Pythagoras' Theorem to obtain the length of the hypotenuse

H2 = 42 + 42 = 16 + 16 = 32    therefore the hypotenuse is sqrt(32)

 

Since that hypotenuse is the diameter of the circle, the radius is half of it, which = (1/2)sqrt(32)

 

The area of the circle is pi times the radius squared. 

 

Area = pi times [(1/2)sqrt(32)]2         This would be so much easier if I knew how to draw a radical on this site. 

 

Anyway, the area ends up being pi times 1/4 of 32 =  8 pi 

 

.

 Apr 16, 2019
 #2
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+1

Let d be the diameter.

\(d^2 = (-1-3)^2 + (-2-2)^2 = 32\)

 

Formula of area of circle: \(A = \dfrac{\pi d^2}{4} = \dfrac{32\pi}{4} = 8\pi\)

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 Apr 18, 2019

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