Question

A circle has a center at (8, 2). The point (3, 7) is on the circle. What is the area of the circle to the nearest tenth of a square unit?

Answer 1

`"Area of the Circle"~~157.1 "sq.unit"`

Explanation:

Point `P(3,7)` is on the Circle having Centre `C(8,2)`.

Therefore, the Distance btwn. pts. `P and C` is the radius `r` of the circle.

:. r^2=(8-3)^2+(2-7)^2=50#.

`:. "Area of the Circle"=pi*r^2~~(3.1416)(50)=157.08~~157.1 "sq.unit"`

Answer 2

157.1 square units.

Explanation:

The area (A) of a circle is.

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(A=pir^2)color(white)(a/a)|)))`
where r is the radius of the circle.

The distance between the centre (8 ,2) and the point (3 ,7) on the circle will be the radius of the circle.

To calculate r, use the `color(blue)"distance formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(r=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))`

let `(x_1,y_1)=(8,2)" and " (x_2,y_2)=(3,7)`

`r=sqrt((3-8)^2+(7-2)^2)=sqrt(25+25)=sqrt50`

`rArrA=pixx(sqrt50)^2=50pi`

Hence area `=50pi≈157.0796≈157.1" nearest tenth"`