Question

a circle is centered at n(-6, -2). the point e(-1, 1) is on the circle. where does the point h(-10, -7) 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For the center $N(-6,-2)$ and point $E(-1,1)$ on the circle, the radius $r$ is:
\[r=\sqrt{(-1 - (-6))^2+(1 - (-2))^2}=\sqrt{(5)^2+(3)^2}=\sqrt{25 + 9}=\sqrt{34}\]

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

For the center $N(-6,-2)$ and point $H(-10,-7)$, the distance $d_{NH}$ is:
\[d_{NH}=\sqrt{(-10-(-6))^2+(-7 - (-2))^2}=\sqrt{(-4)^2+(-5)^2}=\sqrt{16 + 25}=\sqrt{41}\]

Step3: Compare the distances

Since $\sqrt{41}>\sqrt{34}$ (i.e., $d_{NH}>r$), the point $H$ is outside the circle.

Answer:

C. Outside the circle