Question

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Find the radius of a circle whose diameter has endpoints (-3,-2) and K(7,8).

Answer 1

Given:

End points of the diameter are (-3,-2) and (7,8).

To find:

The radius of the circle.

Solution:

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

End points of the diameter are (-3,-2) and (7,8). Using the distance formula, the length of diameter is

`d=√((7-(-3))^2+(8-(-2))^2)`

`d=√((7+3)^2+(8+2)^2)`

`d=√((10)^2+(10)^2)`

`d=√(2(10)^2)`

`d=10√(2)`

So, the diameter is
`10√(2)` units.

We know that, radian of a circle is half of its diameter. So,

`r=(10√(2))/(2)`

`r=5√(2)`

Therefore, the radius of the circle is
`5√(2)` units.