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the endpoints of a diameter of a circle are A (2,1) and B (5,5). find the area of the circle in terms of pi

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apologiabiology

find the distance between them to find diameter
for (x1,y1) and (x2,y2)
D=\(\sqrt{(x2-x1)^2+(y2-y1)^2}\)
for (2,1) and (5,5)
D=\(\sqrt{(5-2)^2+(5-1)^2}\)
D=\(\sqrt{(3)^2+(4)^2}\)
D=\(\sqrt{9+16}\)
D=\(\sqrt{25}\)
D=5


area=pir²
d/2=r
5/2=r=2.5
area=pi2.5²
area=6.25pi

Area of the circle in terms of \(\pi\) =\(\frac{25\pi }{4}\)

Given :

the endpoints of a diameter of a circle are A (2,1) and B (5,5)

Area of the circle=\(\pi r^2\) where 'r' is the radius of the circle

Lets find the length of the diameter using the end points by distance formula

\(AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\A \; is \; (2,1) , B \; is \; (5,5)\\AB=\sqrt{(5-2)^2+(5-1)^2}=\sqrt{25} =5\)

Diameter =5

Radius = diameter /2=\(\frac{5}{2}\)

Area of the circle =\(\pi r^2=\pi (\frac{5}{2})^2=\frac{25\pi }{4}\)

Area of the circle =\(\frac{25\pi }{4}\)

Learn more :   brainly.com/question/15066943

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