Question

What is the radius of a circle with a center at (−9,−1) and a point at (2,8) ?(1 point) units

Answer 1

To find the radius of a circle given its center and a point on the circle, you can use the distance formula. The radius is the distance between the center \((-9, -1)\) and the point \((2, 8)\).

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

In this case, set \((x_1, y_1) = (-9, -1)\) and \((x_2, y_2) = (2, 8)\):

\[
d = \sqrt{(2 - (-9))^2 + (8 - (-1))^2}
\]

Now, calculate each part:

1. \(2 - (-9) = 2 + 9 = 11\)
2. \(8 - (-1) = 8 + 1 = 9\)

Now substitute back into the formula:

\[
d = \sqrt{(11)^2 + (9)^2}
\]
\[
d = \sqrt{121 + 81}
\]
\[
d = \sqrt{202}
\]

So, the radius of the circle is \( \sqrt{202} \) units.