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.

Guest Apr 16, 2019

#1**+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

H^{2} = 4^{2} + 4^{2} = 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

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Guest Apr 16, 2019