Question

He points ​(-9​,-4​) and ​(3​,6​) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.

Answer 1

First end point of the diameter of a circle = ​(-9​,-4​).

Second end point of the diameter of a circle = ​(3​,6​).

Let us find length of the of the diameter of the circle by using distance formula.

We know distance formula,

`d= √((x_2 - x_1)^2+ (y_2 - y_1)^2)`

We have (x1, y1) = ​(-9​,-4​) and (x2,y2) = ​(3​,6​).

Plugging values of x1,y1, x2 and y2 in above distance formula.

`Distance = √((3-(-9))^2+ (6 - (-4))^2)`

=
`√((3+9)^2 +(6+4)^2) = √((12)^2+(10)^2)`

`=√(144+ 100)`

`=√(244)`

Factoring out heighest perfect square from 244.

244= 4* 61.

`√(244) = √(4 * 61)  = √(4) * √(61)`

Square root of 4 is 2.

`√(4) * √(61) = 2 √(61)`

Therefore, diameter of the circle =
`2√(61)`

Radius is half of diameter.

So, dividing value of diameter by 2, we get

Radius =
`(2√(61))/(2)=√(61)`