Question

a circle is centered at o(0, 0) and has a radius of $sqrt{53}$. where does the point v(-3, -7) lie? choose 1 answer: a inside the circle b on the circle c outside the circle

Explanation:

Step1: Calculate distance from origin to point V

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, here $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-3,-7)$. So $d=\sqrt{(-3 - 0)^2+(-7 - 0)^2}=\sqrt{(-3)^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}$.

Step2: Compare distance with radius

Radius of circle $r = \sqrt{53}$. Since $\sqrt{58}>\sqrt{53}$ (because $58>53$), the point is outside the circle.

Answer:

C. Outside the circle