Answer:
area of circle in terms of π is [tex]\mathbf{Area=6.25\:\pi }[/tex]
Step-by-step explanation:
The endpoints of a diameter of a circle are A(3,2) and B(6,6). Find the area of the circle in terms of π.
The formula used to find area of circle is: [tex]Area = \pi r^2[/tex]
We need to find radius of circle. For finding radius we will first find diameter of circle using distance formula.
Finding distance between points A(3,2) and B(6,6) using distance formula.
[tex]Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=3, y_1=2, x_2=6, y_2=6[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-3)^2+(6-2)^2}\\Distance=\sqrt{(3)^2+(4)^2}\\Distance=\sqrt{9+16}\\Distance=\sqrt{25}\\Distance=5[/tex]
So, distance is 5, we can say that diameter of circle = 5
The formula used to find area of circle is: [tex]Area = \pi r^2[/tex]
We need radius, so we know that r = d/2 so, radius = 5/2 = 2.5
Now finding area in terms of π
[tex]Area = \pi r^2\\Area=(2.5)^2\pi \\Area=6.25\:\pi[/tex]
So, area of circle in terms of π is [tex]\mathbf{Area=6.25\:\pi }[/tex]
