Question

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a circle is centered at (d(-1,3)). the point (g(-10,1)) is on the circle.
where does the point (j(-3,12)) lie?
choose 1 answer:
a inside the circle
b on the circle
c outside the circle

Explanation:

Step1: Calculate the radius using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. The center of the circle is $D(-1,3)$ and a point on the circle is $G(-10,1)$. So the radius $r$ is the distance between $D$ and $G$.
$r=\sqrt{(-10+ 1)^2+(1 - 3)^2}=\sqrt{(-9)^2+(-2)^2}=\sqrt{81 + 4}=\sqrt{85}$

Step2: Calculate the distance between the center and point $J$

The center is $D(-1,3)$ and the point is $J(-3,12)$. Using the distance formula, $d_{DJ}=\sqrt{(-3 + 1)^2+(12 - 3)^2}=\sqrt{(-2)^2+9^2}=\sqrt{4+81}=\sqrt{85}$

Answer:

B. On the circle