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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

$d=\sqrt{(7-(-3))^2+(8-(-2))^2}$

$d=\sqrt{(7+3)^2+(8+2)^2}$

$d=\sqrt{(10)^2+(10)^2}$

$d=\sqrt{2(10)^2}$

$d=10\sqrt{2}$

So, the diameter is $10\sqrt{2}$ units.

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

$r=\dfrac{10\sqrt{2}}{2}$

$r=5\sqrt{2}$

Therefore, the radius of the circle is $5\sqrt{2}$ units.